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Recent problems solved by 'ichudov'

ichudov answered: 498 problems
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Quadratic_Equations/34346: Help me solve....please!!!
X^2/x+1+2=1/x+1
1 solutions
Answer 20595 by ichudov(499) About Me  on 2006-04-20 09:02:59 (Show Source):
You can put this solution on YOUR website!
x%5E2%2F%28x%2B1%29%2B2=1%2F%28x%2B1%29
multiply both sides by x+1.
x%5E2%2B2%28x%2B1%29+=+1
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=-1,x=-1.
  • Graphical form: Equation x%5E2%2B2%2A%28x%2B1%29=1 was fully solved.
  • Text form: x^2+2*(x+1)=1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%5E2%2B2%2A%28x%2B1%29=1+%29
    For tutors: simplify_cartoon( x^2+2*(x+1)=1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%5E2%2B2%2A%28x%2B1%29=highlight_red%28+1+%29.
Moved these terms to the left highlight_green%28+-1+%29
It becomes x%5E2%2B2%2A%28x%2B1%29-highlight_green%28+1+%29=0.
Look at x%5E2%2Bhighlight_red%28+2%2A%28x%2B1%29+%29-1=0.
Expanded term 2 by using associative property on %28x%2B1%29
It becomes x%5E2%2Bhighlight_green%28+2%2Ax+%29%2Bhighlight_green%28+2%2A1+%29-1=0.
Look at x%5E2%2B2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29-1=0.
Multiplied numerator integers
It becomes x%5E2%2B2%2Ax%2Bhighlight_green%28+2+%29-1=0.
Look at x%5E2%2B2%2Ax%2Bhighlight_red%28+2+%29-highlight_red%28+1+%29=0.
Added fractions or integers together
It becomes x%5E2%2B2%2Ax%2Bhighlight_green%28+1+%29=0.
Look at highlight_red%28+x%5E2%2B2%2Ax%2B1+%29=0.
Equation highlight_red%28+x%5E2%2B2%2Ax%2B1=0+%29 is a quadratic equation: x^2+2*x+1 =0, and has solutions -1,-1
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-1,x=-1.

Universal Simplifier and Solver


Done!

Mixture_Word_Problems/34226: 6%2Fx%2B18%2Fx%2B8=8
solve to find X (there maybe 1 answer or 2)
1 solutions
Answer 20516 by ichudov(499) About Me  on 2006-04-19 12:18:35 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 6%2Fx%2B18%2Fx%2B8=8 simplifies to 24%2Fx=0
  • Text form: 6/x+18/x+8=8 simplifies to 24/x=0
  • Cartoon (animation) form: simplify_cartoon%28+6%2Fx%2B18%2Fx%2B8=8+%29
    For tutors: simplify_cartoon( 6/x+18/x+8=8 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+6%2Fx+%29%2Bhighlight_red%28+18%2Fx+%29%2B8=8.
Eliminated similar terms highlight_red%28+6%2Fx+%29,highlight_red%28+18%2Fx+%29 replacing them with highlight_green%28+%286%2B18%29%2Fx+%29
It becomes highlight_green%28+%286%2B18%29%2Fx+%29%2B8=8.
Look at %28highlight_red%28+6+%29%2Bhighlight_red%28+18+%29%29%2Fx%2B8=8.
Added fractions or integers together
It becomes %28highlight_green%28+24+%29%29%2Fx%2B8=8.
Look at highlight_red%28+%28highlight_red%28+24+%29%29%2Fx+%29%2B8=8.
Remove unneeded parentheses around factor highlight_red%28+24+%29
It becomes highlight_green%28+24+%29%2Fx%2B8=8.
Look at 24%2Fx%2B8=highlight_red%28+8+%29.
Moved these terms to the left highlight_green%28+-8+%29
It becomes 24%2Fx%2B8-highlight_green%28+8+%29=0.
Look at 24%2Fx%2Bhighlight_red%28+8+%29-highlight_red%28+8+%29=0.
Added fractions or integers together
It becomes 24%2Fx%2Bhighlight_green%28+0+%29=0.
Look at 24%2Fx%2Bhighlight_red%28+0+%29=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes 24%2Fx=0.
Result: 24%2Fx=0

Universal Simplifier and Solver


Done!


equation simplifies to 24%2Fx+=+0, which has no solutions.

Percentage-and-ratio-word-problems/34224: This question is from textbook
Help! :o( This word problem should be so simple, I know-but I'm having a hard time comprehending it enough to wright a correct expression. Here's the problem: John Debuzzi used to read p words per minute. After taking a speed reading course, his speed increased by 60 words per minute. Write an expression that represents his new reading speed.
1 solutions
Answer 20512 by ichudov(499) About Me  on 2006-04-19 11:59:37 (Show Source):
You can put this solution on YOUR website!
He was able to read p words per minute
after taking the course he was able to read p plus sixty words
p+60 is the expression

Trigonometry-basics/34208: Find A, when a = 7 and b = 12.
1 solutions
Answer 20504 by ichudov(499) About Me  on 2006-04-19 08:56:05 (Show Source):
You can put this solution on YOUR website!
We are not mind readers here, we do not know what A, a and b you are talking about

Trigonometry-basics/34207: 2/3 radians is how much degreees exactly?
1 solutions
Answer 20503 by ichudov(499) About Me  on 2006-04-19 08:54:44 (Show Source):
You can put this solution on YOUR website!
there is 2pi radians in the whole circle (360 degrees). 60 degrees is 1%2F6 of 360 degrees, so, 60 degrees is 2pi%2F6+=+pi%2F3 radians

Polynomials-and-rational-expressions/34138: Simplify the following
(x+4)^2/x+5 times x-4/x^2-16
/ indicates fraction
1 solutions
Answer 20453 by ichudov(499) About Me  on 2006-04-18 20:48:33 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: %28%28x%2B4%29%5E2%2F%28x%2B5%29%29%2A%28%28x-4%29%2F%28x%5E2-16%29%29 simplifies to %28x%2B4%29%2F%28x%2B5%29
  • Text form: ((x+4)^2/(x+5))*((x-4)/(x^2-16)) simplifies to (x+4)/(x+5)
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( ((x+4)^2/(x+5))*((x-4)/(x^2-16)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor highlight_red%28+%28x%2B4%29%5E2+%29,highlight_red%28+1%2F%28x%2B5%29+%29
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+%28x-4%29+%29,highlight_red%28+1%2F%28x%5E2-16%29+%29
It becomes .
Look at .
Canceled out common factors (x-(-4))
Look at %28x%2B4%29%2F%28x%2B5%29%2Ahighlight_red%28+%28x-4%29+%29%2Fhighlight_red%28+%28x-4%29+%29.
Reduce similar several occurrences of highlight_red%28+%28x-4%29+%29 to
It becomes %28x%2B4%29%2F%28x%2B5%29.
Result: %28x%2B4%29%2F%28x%2B5%29

Universal Simplifier and Solver


Done!

Polynomials-and-rational-expressions/34133: simplyify the following complex fraction:
1+2/3
-------
7/6
1 solutions
Answer 20452 by ichudov(499) About Me  on 2006-04-18 20:45:47 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: %281%2B2%2F3%29%2F%287%2F6%29 simplifies to 10%2F7
  • Text form: (1+2/3)/(7/6) simplifies to 10/7
  • Cartoon (animation) form: simplify_cartoon%28+%281%2B2%2F3%29%2F%287%2F6%29+%29
    For tutors: simplify_cartoon( (1+2/3)/(7/6) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%281%2B2%2F3%29%2F%28highlight_red%28+7%2F6+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F7+%29,highlight_red%28+6+%29
It becomes %281%2B2%2F3%29%2Fhighlight_green%28+7+%29%2Ahighlight_green%28+6+%29.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+2%2F3+%29%29%2F7%2A6.
Added fractions or integers together
It becomes %28highlight_green%28+5%2F3+%29%29%2F7%2A6.
Look at highlight_red%28+%28highlight_red%28+5%2F3+%29%29%2F7%2A6+%29.
Remove unneeded parentheses around factor highlight_red%28+5+%29,highlight_red%28+1%2F3+%29
It becomes highlight_green%28+5+%29%2Fhighlight_green%28+3+%29%2F7%2A6.
Look at 5%2Fhighlight_red%28+3+%29%2F7%2Ahighlight_red%28+6+%29.
Factors 6 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes 5%2Fhighlight_green%28+1+%29%2F7%2Ahighlight_green%28+2+%29.
Look at highlight_red%28+5+%29%2F1%2F7%2Ahighlight_red%28+2+%29.
Multiplied numerator integers
It becomes highlight_green%28+10+%29%2F1%2F7.
Look at 10%2Fhighlight_red%28+1+%29%2Fhighlight_red%28+7+%29.
Multiplied denominator integers
It becomes 10%2Fhighlight_green%28+7+%29.
Result: 10%2F7

Universal Simplifier and Solver


Done!

Polynomials-and-rational-expressions/34131: Simplify:
x+8
-------
x^2-64
1 solutions
Answer 20451 by ichudov(499) About Me  on 2006-04-18 20:41:31 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: %28x%2B8%29%2F%28x%5E2-64%29 simplifies to 1%2F%28x-8%29
  • Text form: (x+8)/(x^2-64) simplifies to 1/(x-8)
  • Cartoon (animation) form: simplify_cartoon%28+%28x%2B8%29%2F%28x%5E2-64%29+%29
    For tutors: simplify_cartoon( (x+8)/(x^2-64) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28x%2B8%29+%29%2Fhighlight_red%28+%28x%5E2-64%29+%29.
Canceled out common factors (x-(-8))
Look at highlight_red%28+%28highlight_red%28+1+%29%29%2F%28x-8%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes highlight_green%28+1+%29%2F%28x-8%29.
Result: 1%2F%28x-8%29

Universal Simplifier and Solver


Done!

Rational-functions/34046: 3/x+2/y / 2/x - 3/y = ?
1 solutions
Answer 20410 by ichudov(499) About Me  on 2006-04-18 13:54:58 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 3%2Fx%2B%282%2Fy%29%2F%282%2Fx%29-3%2Fy simplifies to 3%2Fx%2Bx%2Fy-3%2Fy
  • Text form: 3/x+(2/y)/(2/x)-3/y simplifies to 3/x+x/y-3/y
  • Cartoon (animation) form: simplify_cartoon%28+3%2Fx%2B%282%2Fy%29%2F%282%2Fx%29-3%2Fy+%29
    For tutors: simplify_cartoon( 3/x+(2/y)/(2/x)-3/y )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2Fx%2Bhighlight_red%28+%28highlight_red%28+2%2Fy+%29%29%2F%282%2Fx%29+%29-3%2Fy.
Remove unneeded parentheses around factor highlight_red%28+2+%29,highlight_red%28+1%2Fy+%29
It becomes 3%2Fx%2Bhighlight_green%28+2+%29%2Fhighlight_green%28+y+%29%2F%282%2Fx%29-3%2Fy.
Look at 3%2Fx%2Bhighlight_red%28+2%2Fy%2F%28highlight_red%28+2%2Fx+%29%29+%29-3%2Fy.
Remove unneeded parentheses around factor highlight_red%28+1%2F2+%29,highlight_red%28+x+%29
It becomes 3%2Fx%2B2%2Fy%2Fhighlight_green%28+2+%29%2Ahighlight_green%28+x+%29-3%2Fy.
Look at 3%2Fx%2Bhighlight_red%28+2+%29%2Fy%2Fhighlight_red%28+2+%29%2Ax-3%2Fy.
Factors 2 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 3%2Fx%2Bhighlight_green%28+1+%29%2Fy%2Fhighlight_green%28+1+%29%2Ax-3%2Fy.
Look at 3%2Fx%2Bhighlight_red%28+1+%29%2Fy%2Fhighlight_red%28+1+%29%2Ax-3%2Fy.
Reduce similar several occurrences of highlight_red%28+1+%29 to
It becomes 3%2Fx%2B1%2Fy%2Ax-3%2Fy.
Look at 3%2Fx%2Bhighlight_red%28+1+%29%2Fy%2Ax-3%2Fy.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 3%2Fx%2Bx%2Fy-3%2Fy.
Result: 3%2Fx%2Bx%2Fy-3%2Fy

Universal Simplifier and Solver


Done!

Points-lines-and-rays/34048: could someone explain to me how to find the perimeter of a square that has a side measure of 45 cm.Do I multiply 45 x 4? Thanks
1 solutions
Answer 20409 by ichudov(499) About Me  on 2006-04-18 13:54:08 (Show Source):
You can put this solution on YOUR website!
Yes, you multiply 45 by 4, since perimeter is sum of the lengths of all sides and squares have four equal sides.

Linear-equations/34045: This question is from textbook
I entered the wrong email address, so if this one's probably out in cyberspace somewhere. So here it is again:

Can someone give me a step by step of how to solve this?
-27.23+x=9.77
1 solutions
Answer 20402 by ichudov(499) About Me  on 2006-04-18 13:24:09 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=37.
  • Graphical form: Equation -27.23%2Bx=9.77 was fully solved.
  • Text form: -27.23+x=9.77 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-27.23%2Bx=9.77+%29
    For tutors: simplify_cartoon( -27.23+x=9.77 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -highlight_red%28+27.23+%29%2Bx=9.77.
Moved -27.23 to the right of expression
It becomes x-highlight_green%28+27.23+%29=9.77.
Look at x-27.23=highlight_red%28+9.77+%29.
Moved these terms to the left highlight_green%28+-9.77+%29
It becomes x-27.23-highlight_green%28+9.77+%29=0.
Look at x-highlight_red%28+27.23+%29-highlight_red%28+9.77+%29=0.
Added fractions or integers together
It becomes x-highlight_green%28+3700%2F100+%29=0.
Look at x-highlight_red%28+3700+%29%2Fhighlight_red%28+100+%29=0.
Factors 3700 and 100 have greatest common factor (GCF) of 100. Reducing fraction.
It becomes x-highlight_green%28+37+%29%2Fhighlight_green%28+1+%29=0.
Look at x-37%2Fhighlight_red%28+1+%29=0.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes x-37=0.
Look at highlight_red%28+x-37+%29=0.
Solved linear equation highlight_red%28+x-37=0+%29 equivalent to x-37 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=37.

Universal Simplifier and Solver


Done!

Equations/34039: This question is from textbook pre-algebra
20.6+2.1x=-8.2x
1 solutions
Answer 20392 by ichudov(499) About Me  on 2006-04-18 12:37:00 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=-2.
  • Graphical form: Equation 20.6%2B2.1x=-8.2x was fully solved.
  • Text form: 20.6+2.1x=-8.2x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+20.6%2B2.1x=-8.2x+%29
    For tutors: simplify_cartoon( 20.6+2.1x=-8.2x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+20.6+%29%2B2.1%2Ax=-8.2x.
Moved 20.6 to the right of expression
It becomes 2.1%2Ax%2Bhighlight_green%28+20.6+%29=-8.2x.
Look at 2.1%2Ax%2B20.6=highlight_red%28+-8.2%2Ax+%29.
Moved these terms to the left highlight_green%28+8.2%2Ax+%29
It becomes 2.1%2Ax%2B20.6%2Bhighlight_green%28+8.2%2Ax+%29=0.
Look at 2.1%2Ax%2Bhighlight_red%28+20.6+%29%2B8.2%2Ax=0.
Moved 20.6 to the right of expression
It becomes 2.1%2Ax%2B8.2%2Ax%2Bhighlight_green%28+20.6+%29=0.
Look at highlight_red%28+2.1%2Ax+%29%2Bhighlight_red%28+8.2%2Ax+%29%2B20.6=0.
Eliminated similar terms highlight_red%28+2.1%2Ax+%29,highlight_red%28+8.2%2Ax+%29 replacing them with highlight_green%28+%282.1%2B8.2%29%2Ax+%29
It becomes highlight_green%28+%282.1%2B8.2%29%2Ax+%29%2B20.6=0.
Look at %28highlight_red%28+2.1+%29%2Bhighlight_red%28+8.2+%29%29%2Ax%2B20.6=0.
Added fractions or integers together
It becomes %28highlight_green%28+103%2F10+%29%29%2Ax%2B20.6=0.
Look at highlight_red%28+%28highlight_red%28+103%2F10+%29%29%2Ax+%29%2B20.6=0.
Remove unneeded parentheses around factor highlight_red%28+103+%29,highlight_red%28+1%2F10+%29
It becomes highlight_green%28+103+%29%2Fhighlight_green%28+10+%29%2Ax%2B20.6=0.
Look at highlight_red%28+103%2F10%2Ax%2B20.6+%29=0.
Solved linear equation highlight_red%28+103%2F10%2Ax%2B20.6=0+%29 equivalent to 10.3*x+20.6 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-2.

Universal Simplifier and Solver


Done!

Equations/34040: -(x+6)+4x=3(x-1)+7
1 solutions
Answer 20391 by ichudov(499) About Me  on 2006-04-18 12:36:24 (Show Source):
You can put this solution on YOUR website!
This equation has no solutions. It simplifies to 0=10.
Are you sure that you typed it correctly?
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: -%28x%2B6%29%2B4x=3%2A%28x-1%29%2B7 simplifies to -10=0
  • Text form: -(x+6)+4x=3*(x-1)+7 simplifies to -10=0
  • Cartoon (animation) form: simplify_cartoon%28+-%28x%2B6%29%2B4x=3%2A%28x-1%29%2B7+%29
    For tutors: simplify_cartoon( -(x+6)+4x=3*(x-1)+7 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -highlight_red%28+%28x%2B6%29+%29%2B4%2Ax=3%2A%28x-1%29%2B7.
Remove unneeded parentheses around terms highlight_red%28+-x+%29,highlight_red%28+-6+%29
It becomes -highlight_green%28+x+%29-highlight_green%28+6+%29%2B4%2Ax=3%2A%28x-1%29%2B7.
Look at -x-highlight_red%28+6+%29%2B4%2Ax=3%2A%28x-1%29%2B7.
Moved -6 to the right of expression
It becomes -x%2B4%2Ax-highlight_green%28+6+%29=3%2A%28x-1%29%2B7.
Look at -highlight_red%28+x+%29%2Bhighlight_red%28+4%2Ax+%29-6=3%2A%28x-1%29%2B7.
Eliminated similar terms highlight_red%28+-x+%29,highlight_red%28+4%2Ax+%29 replacing them with highlight_green%28+%28-1%2B4%29%2Ax+%29
It becomes highlight_green%28+%28-1%2B4%29%2Ax+%29-6=3%2A%28x-1%29%2B7.
Look at %28-highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2Ax-6=3%2A%28x-1%29%2B7.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-6=3%2A%28x-1%29%2B7.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-6=3%2A%28x-1%29%2B7.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-6=3%2A%28x-1%29%2B7.
Look at 3%2Ax-6=highlight_red%28+3%2A%28x-1%29%2B7+%29.
Moved these terms to the left highlight_green%28+-3%2A%28x-1%29+%29,highlight_green%28+-7+%29
It becomes 3%2Ax-6-highlight_green%28+3%2A%28x-1%29+%29-highlight_green%28+7+%29=0.
Look at 3%2Ax-highlight_red%28+6+%29-3%2A%28x-1%29-highlight_red%28+7+%29=0.
Added fractions or integers together
It becomes 3%2Ax%2Bhighlight_green%28+-13+%29-3%2A%28x-1%29=0.
Look at 3%2Ax%2Bhighlight_red%28+-13+%29-3%2A%28x-1%29=0.
Moved -13 to the right of expression
It becomes 3%2Ax-3%2A%28x-1%29%2Bhighlight_green%28+-13+%29=0.
Look at 3%2Ax-3%2A%28x-1%29%2Bhighlight_red%28+-13+%29=0.
Removed extra sign in front of -13
It becomes 3%2Ax-3%2A%28x-1%29-highlight_green%28+13+%29=0.
Look at 3%2Ax-highlight_red%28+3%2A%28x-1%29+%29-13=0.
Expanded term -3 by using associative property on %28x-1%29
It becomes 3%2Ax-highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+3%2A1+%29-13=0.
Look at 3%2Ax-3%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29-13=0.
Multiplied numerator integers
It becomes 3%2Ax-3%2Ax%2Bhighlight_green%28+3+%29-13=0.
Look at 3%2Ax-3%2Ax%2Bhighlight_red%28+3+%29-highlight_red%28+13+%29=0.
Added fractions or integers together
It becomes 3%2Ax-3%2Ax%2Bhighlight_green%28+-10+%29=0.
Look at 3%2Ax-3%2Ax%2Bhighlight_red%28+-10+%29=0.
Removed extra sign in front of -10
It becomes 3%2Ax-3%2Ax-highlight_green%28+10+%29=0.
Look at highlight_red%28+3%2Ax+%29-highlight_red%28+3%2Ax+%29-10=0.
Eliminated similar terms highlight_red%28+3%2Ax+%29,highlight_red%28+-3%2Ax+%29 replacing them with highlight_green%28+%283-3%29%2Ax+%29
It becomes highlight_green%28+%283-3%29%2Ax+%29-10=0.
Look at highlight_red%28+%283-3%29%2Ax+%29-10=0.
Since highlight_red%28+%283-3%29%2Ax+%29 has zero as a factor, it should be replaced with a zero
Look at 0-10=0.
Added fractions or integers together
It becomes 0-10=0.
Look at highlight_red%28+0+%29-10=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes -10=0.
Result: -10=0

Universal Simplifier and Solver


Done!

Linear-equations/34029: This question is from textbook Elementary and Intermediate Algebra
I don't understand how to solve linear equations. What is 'a' in this problem?
-a/8=-7
1 solutions
Answer 20381 by ichudov(499) About Me  on 2006-04-18 11:51:48 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: a=56.
  • Graphical form: Equation -a%2F8=-7 was fully solved.
  • Text form: -a/8=-7 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-a%2F8=-7+%29
    For tutors: simplify_cartoon( -a/8=-7 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -a%2F8=highlight_red%28+-7+%29.
Moved these terms to the left highlight_green%28+7+%29
It becomes -a%2F8%2Bhighlight_green%28+7+%29=0.
Look at highlight_red%28+-a%2F8%2B7+%29=0.
Solved linear equation highlight_red%28+-a%2F8%2B7=0+%29 equivalent to -0.125*a+7 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=56.

Universal Simplifier and Solver


Done!

Quadratic_Equations/33875: use the discriminant to determine whether(((x^2-6x=-15)))has one real solution, two real number solutions or two complex number solutions
1 solutions
Answer 20281 by ichudov(499) About Me  on 2006-04-17 14:21:37 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B15+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A1%2A15=-24.

The discriminant -24 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -24 is + or - sqrt%28+24%29+=+4.89897948556636.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B15+%29

Linear-equations/33870: This question is from textbook Elementary and Intermediate Algebra
Can someone help me solve this problem?
-5a+3=2a+10
1 solutions
Answer 20274 by ichudov(499) About Me  on 2006-04-17 13:21:23 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: a=-1.
  • Graphical form: Equation -5a%2B3=2a%2B10 was fully solved.
  • Text form: -5a+3=2a+10 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-5a%2B3=2a%2B10+%29
    For tutors: simplify_cartoon( -5a+3=2a+10 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -5%2Aa%2B3=highlight_red%28+2%2Aa%2B10+%29.
Moved these terms to the left highlight_green%28+-2%2Aa+%29,highlight_green%28+-10+%29
It becomes -5%2Aa%2B3-highlight_green%28+2%2Aa+%29-highlight_green%28+10+%29=0.
Look at -5%2Aa%2Bhighlight_red%28+3+%29-2%2Aa-highlight_red%28+10+%29=0.
Added fractions or integers together
It becomes -5%2Aa%2Bhighlight_green%28+-7+%29-2%2Aa=0.
Look at -5%2Aa%2Bhighlight_red%28+-7+%29-2%2Aa=0.
Moved -7 to the right of expression
It becomes -5%2Aa-2%2Aa%2Bhighlight_green%28+-7+%29=0.
Look at -5%2Aa-2%2Aa%2Bhighlight_red%28+-7+%29=0.
Removed extra sign in front of -7
It becomes -5%2Aa-2%2Aa-highlight_green%28+7+%29=0.
Look at -highlight_red%28+5%2Aa+%29-highlight_red%28+2%2Aa+%29-7=0.
Eliminated similar terms highlight_red%28+-5%2Aa+%29,highlight_red%28+-2%2Aa+%29 replacing them with highlight_green%28+%28-5-2%29%2Aa+%29
It becomes highlight_green%28+%28-5-2%29%2Aa+%29-7=0.
Look at %28-highlight_red%28+5+%29-highlight_red%28+2+%29%29%2Aa-7=0.
Added fractions or integers together
It becomes %28highlight_green%28+-7+%29%29%2Aa-7=0.
Look at %28highlight_red%28+-7+%29%29%2Aa-7=0.
Removed extra sign in front of -7
It becomes %28-highlight_green%28+7+%29%29%2Aa-7=0.
Look at highlight_red%28+%28-highlight_red%28+7+%29%29%2Aa+%29-7=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes -highlight_green%28+7+%29%2Aa-7=0.
Look at highlight_red%28+-7%2Aa-7+%29=0.
Solved linear equation highlight_red%28+-7%2Aa-7=0+%29 equivalent to -7*a-7 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=-1.

Universal Simplifier and Solver


Done!

Linear-equations/33871: This question is from textbook Elementary and Intermediate Algebra
what is x here?

14=3+2x
1 solutions
Answer 20273 by ichudov(499) About Me  on 2006-04-17 13:20:56 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=5.5.
  • Graphical form: Equation 14=3%2B2x was fully solved.
  • Text form: 14=3+2x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+14=3%2B2x+%29
    For tutors: simplify_cartoon( 14=3+2x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 14=highlight_red%28+3+%29%2B2%2Ax.
Moved 3 to the right of expression
It becomes 14=2%2Ax%2Bhighlight_green%28+3+%29.
Look at 14=highlight_red%28+2%2Ax%2B3+%29.
Moved these terms to the left highlight_green%28+-2%2Ax+%29,highlight_green%28+-3+%29
It becomes 14-highlight_green%28+2%2Ax+%29-highlight_green%28+3+%29=0.
Look at highlight_red%28+14+%29-2%2Ax-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes highlight_green%28+11+%29-2%2Ax=0.
Look at highlight_red%28+11+%29-2%2Ax=0.
Moved 11 to the right of expression
It becomes -2%2Ax%2Bhighlight_green%28+11+%29=0.
Look at highlight_red%28+-2%2Ax%2B11+%29=0.
Solved linear equation highlight_red%28+-2%2Ax%2B11=0+%29 equivalent to -2*x+11 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=5.5.

Universal Simplifier and Solver


Done!

Linear-equations/33867: This question is from textbook
How do I solve 2(2r-4)/5=3r+6/4-3/2
1 solutions
Answer 20270 by ichudov(499) About Me  on 2006-04-17 12:45:22 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: r=-0.727272727272727.
  • Graphical form: Equation 2%2A%282r-4%29%2F5=3r%2B6%2F4-3%2F2 was fully solved.
  • Text form: 2*(2r-4)/5=3r+6/4-3/2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%282r-4%29%2F5=3r%2B6%2F4-3%2F2+%29
    For tutors: simplify_cartoon( 2*(2r-4)/5=3r+6/4-3/2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_red%28+6+%29%2Fhighlight_red%28+4+%29-3%2F2.
Factors 6 and 4 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_green%28+3+%29%2Fhighlight_green%28+2+%29-3%2F2.
Look at 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_red%28+3%2F2+%29-highlight_red%28+3%2F2+%29.
Added fractions or integers together
It becomes 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_green%28+0%2F2+%29.
Look at 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_red%28+0+%29%2Fhighlight_red%28+2+%29.
Factors 0 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_green%28+0+%29%2Fhighlight_green%28+1+%29.
Look at 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_red%28+0%2F1+%29.
Remove extraneous zero highlight_red%28+0%2F1+%29
It becomes 2%2A%282%2Ar-4%29%2F5=3%2Ar.
Look at 2%2A%282%2Ar-4%29%2F5=highlight_red%28+3%2Ar+%29.
Moved these terms to the left highlight_green%28+-3%2Ar+%29
It becomes 2%2A%282%2Ar-4%29%2F5-highlight_green%28+3%2Ar+%29=0.
Look at highlight_red%28+2%2A%282%2Ar-4%29%2F5+%29-3%2Ar=0.
Expanded term 2%2F5 by using associative property on %282%2Ar-4%29
It becomes highlight_green%28+2%2F5%2A2%2Ar+%29-highlight_green%28+2%2F5%2A4+%29-3%2Ar=0.
Look at highlight_red%28+2+%29%2F5%2Ahighlight_red%28+2+%29%2Ar-2%2F5%2A4-3%2Ar=0.
Multiplied numerator integers
It becomes highlight_green%28+4+%29%2F5%2Ar-2%2F5%2A4-3%2Ar=0.
Look at 4%2F5%2Ar-highlight_red%28+2+%29%2F5%2Ahighlight_red%28+4+%29-3%2Ar=0.
Multiplied numerator integers
It becomes 4%2F5%2Ar-highlight_green%28+8+%29%2F5-3%2Ar=0.
Look at 4%2F5%2Ar-highlight_red%28+8%2F5+%29-3%2Ar=0.
Moved -8%2F5 to the right of expression
It becomes 4%2F5%2Ar-3%2Ar-highlight_green%28+8%2F5+%29=0.
Look at highlight_red%28+4%2F5%2Ar+%29-highlight_red%28+3%2Ar+%29-8%2F5=0.
Eliminated similar terms highlight_red%28+4%2F5%2Ar+%29,highlight_red%28+-3%2Ar+%29 replacing them with highlight_green%28+%284%2A1%2F5-3%29%2Ar+%29
It becomes highlight_green%28+%284%2A1%2F5-3%29%2Ar+%29-8%2F5=0.
Look at %28highlight_red%28+4+%29%2Ahighlight_red%28+1+%29%2F5-3%29%2Ar-8%2F5=0.
Multiplied numerator integers
It becomes %28highlight_green%28+4+%29%2F5-3%29%2Ar-8%2F5=0.
Look at %28highlight_red%28+4%2F5+%29-highlight_red%28+3+%29%29%2Ar-8%2F5=0.
Added fractions or integers together
It becomes %28-highlight_green%28+11%2F5+%29%29%2Ar-8%2F5=0.
Look at highlight_red%28+%28-highlight_red%28+11%2F5+%29%29%2Ar+%29-8%2F5=0.
Remove unneeded parentheses around factor highlight_red%28+11+%29,highlight_red%28+1%2F5+%29
It becomes -highlight_green%28+11+%29%2Fhighlight_green%28+5+%29%2Ar-8%2F5=0.
Look at highlight_red%28+-11%2F5%2Ar-8%2F5+%29=0.
Solved linear equation highlight_red%28+-11%2F5%2Ar-8%2F5=0+%29 equivalent to -2.2*r-1.6 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: r=-0.727272727272727.

Universal Simplifier and Solver


Done!

Linear-equations/33866: This question is from textbook
I need to solve this.
-3+3x=-2(x+1)
1 solutions
Answer 20269 by ichudov(499) About Me  on 2006-04-17 12:40:14 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=0.2.
  • Graphical form: Equation -3%2B3x=-2%2A%28x%2B1%29 was fully solved.
  • Text form: -3+3x=-2*(x+1) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-3%2B3x=-2%2A%28x%2B1%29+%29
    For tutors: simplify_cartoon( -3+3x=-2*(x+1) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -highlight_red%28+3+%29%2B3%2Ax=-2%2A%28x%2B1%29.
Moved -3 to the right of expression
It becomes 3%2Ax-highlight_green%28+3+%29=-2%2A%28x%2B1%29.
Look at 3%2Ax-3=highlight_red%28+-2%2A%28x%2B1%29+%29.
Moved these terms to the left highlight_green%28+2%2A%28x%2B1%29+%29
It becomes 3%2Ax-3%2Bhighlight_green%28+2%2A%28x%2B1%29+%29=0.
Look at 3%2Ax-highlight_red%28+3+%29%2B2%2A%28x%2B1%29=0.
Moved -3 to the right of expression
It becomes 3%2Ax%2B2%2A%28x%2B1%29-highlight_green%28+3+%29=0.
Look at 3%2Ax%2Bhighlight_red%28+2%2A%28x%2B1%29+%29-3=0.
Expanded term 2 by using associative property on %28x%2B1%29
It becomes 3%2Ax%2Bhighlight_green%28+2%2Ax+%29%2Bhighlight_green%28+2%2A1+%29-3=0.
Look at 3%2Ax%2B2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29-3=0.
Multiplied numerator integers
It becomes 3%2Ax%2B2%2Ax%2Bhighlight_green%28+2+%29-3=0.
Look at 3%2Ax%2B2%2Ax%2Bhighlight_red%28+2+%29-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes 3%2Ax%2B2%2Ax%2Bhighlight_green%28+-1+%29=0.
Look at 3%2Ax%2B2%2Ax%2Bhighlight_red%28+-1+%29=0.
Removed extra sign in front of -1
It becomes 3%2Ax%2B2%2Ax-highlight_green%28+1+%29=0.
Look at highlight_red%28+3%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29-1=0.
Eliminated similar terms highlight_red%28+3%2Ax+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%283%2B2%29%2Ax+%29
It becomes highlight_green%28+%283%2B2%29%2Ax+%29-1=0.
Look at %28highlight_red%28+3+%29%2Bhighlight_red%28+2+%29%29%2Ax-1=0.
Added fractions or integers together
It becomes %28highlight_green%28+5+%29%29%2Ax-1=0.
Look at highlight_red%28+%28highlight_red%28+5+%29%29%2Ax+%29-1=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes highlight_green%28+5+%29%2Ax-1=0.
Look at highlight_red%28+5%2Ax-1+%29=0.
Solved linear equation highlight_red%28+5%2Ax-1=0+%29 equivalent to 5*x-1 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=0.2.

Universal Simplifier and Solver


Done!

Quadratic_Equations/30987: This question is from textbook College Algebra
Solve equation
%285x-1%29%5E%282%2F3%29+-5%285x-1%29%5E%281%2F3%29+%2B+4=0
1 solutions
Answer 17714 by ichudov(499) About Me  on 2006-03-22 06:18:38 (Show Source):
You can put this solution on YOUR website!
This is a "substitution" problem. Note the common element in your equation, 5x-1%29%5E%281%2F3%29. For simplicity, just replate it with y:
y%5E2-5y%2B4+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B-5y%2B4+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A1%2A4=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+9+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+9+%29%29%2F2%5C1+=+4
y%5B2%5D+=+%28-%28-5%29-sqrt%28+9+%29%29%2F2%5C1+=+1

Quadratic expression 1y%5E2%2B-5y%2B4 can be factored:
1y%5E2%2B-5y%2B4+=+1%28y-4%29%2A%28y-1%29
Again, the answer is: 4, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B4+%29


So, y = 1 or y = 4.
system%28+5x-1%29%5E%281%2F3%29+=+1%2C+%285x-1%29%5E%281%2F3%29+=+4%29+
take to third degree
system%28+5x-1+=+1%5E3%2C+5x-1+=+4%5E3%29+
system%28+5x-1+=+1%2C+5x-1+=+64%29+
add one
system%28+5x+=+2%2C+5x+=+65%29+
system%28+x+=+2%2F5%2C+x+=+13+%29+
please double check my solution

Geometric_formulas/30994: This question is from textbook
What is Precision? and What is the Precision for 80 inches? Thank You for your help
1 solutions
Answer 17713 by ichudov(499) About Me  on 2006-03-22 06:02:41 (Show Source):

Trigonometry-basics/30955: This question is from textbook Algebra 2
solve triangle ABC using the diagram and the given measurements....
B=41 degrees, a=6.8
..A
..|..\
.b|...\ c
..|.....\
..|____\
..C a B
1 solutions
Answer 17682 by ichudov(499) About Me  on 2006-03-21 19:02:57 (Show Source):
You can put this solution on YOUR website!
The formulas are as follows:
b = a tan B
c+=+a%2Fcos%28B%29
Use your calculator to find out the cosine and tangent.

Polynomials-and-rational-expressions/30915: This question is from textbook Algebra Structure and Method Book 1
6+x-x^2 / x^2-13x+42 divided by 2x^2-5x-3 / 2x^2-13x-7
1 solutions
Answer 17662 by ichudov(499) About Me  on 2006-03-21 16:23:29 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: simplifies to %28-x-2%29%2F%28x-6%29
  • Text form: ((6+x-x^2)/(x^2-13x+42))/((2x^2-5x-3)/(2x^2-13x-7)) simplifies to (-x-2)/(x-6)
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( ((6+x-x^2)/(x^2-13x+42))/((2x^2-5x-3)/(2x^2-13x-7)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor highlight_red%28+%286%2Bx-x%5E2%29+%29,highlight_red%28+1%2F%28x%5E2-13%2Ax%2B42%29+%29
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+1%2F%282%2Ax%5E2-5%2Ax-3%29+%29,highlight_red%28+%282%2Ax%5E2-13%2Ax-7%29+%29
It becomes .
Look at .
Moved 6 to the right of expression
It becomes .
Look at .
Canceled out common factors (x-(3))
Look at .
Canceled out common factors (x-(7))
Look at .
Reduce similar several occurrences of highlight_red%28+1%2F%282%2Ax%2B1%29+%29 to
It becomes %28-x-2%29%2F%28x-6%29.
Result: %28-x-2%29%2F%28x-6%29

Universal Simplifier and Solver


Done!

Polynomials-and-rational-expressions/30909: This question is from textbook Elementary and Intermediate Algebra
a%5E2-2a-35
1 solutions
Answer 17651 by ichudov(499) About Me  on 2006-03-21 14:26:05 (Show Source):
You can put this solution on YOUR website!
Great job on specifying your textbook! Your question received priority treatment.
It is not clear what you wanted, but if you wanted to factorise it, you can try to use the quadratic solver. It gives you factorisation among other things:


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 1a%5E2%2B-2a%2B-35+=+0) has the following solutons:

a%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-35=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+144+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+7
a%5B2%5D+=+%28-%28-2%29-sqrt%28+144+%29%29%2F2%5C1+=+-5

Quadratic expression 1a%5E2%2B-2a%2B-35 can be factored:
1a%5E2%2B-2a%2B-35+=+1%28a-7%29%2A%28a--5%29
Again, the answer is: 7, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-35+%29

Rational-functions/30780: -2x^2-5x/x^2-7x + x-2/x+7 + 2x-3/x
1 solutions
Answer 17508 by ichudov(499) About Me  on 2006-03-20 10:37:59 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: -2x%5E2-5x%2Fx%5E2-7x%2Bx-2%2Fx%2B7%2B2x-3%2Fx simplifies to -2%2Ax%5E2-10%2Fx-4%2Ax%2B7
  • Text form: -2x^2-5x/x^2-7x+x-2/x+7+2x-3/x simplifies to -2*x^2-10/x-4*x+7
  • Cartoon (animation) form: simplify_cartoon%28+-2x%5E2-5x%2Fx%5E2-7x%2Bx-2%2Fx%2B7%2B2x-3%2Fx+%29
    For tutors: simplify_cartoon( -2x^2-5x/x^2-7x+x-2/x+7+2x-3/x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E%281-2%29+%29
It becomes -2%2Ax%5E2-5%2Ahighlight_green%28+x%5E%281-2%29+%29-7%2Ax%2Bx-2%2Fx%2B7%2B2%2Ax-3%2Fx.
Look at -2%2Ax%5E2-5%2Ax%5E%281-2%29-7%2Ax%2Bx-2%2Fx%2Bhighlight_red%28+7+%29%2B2%2Ax-3%2Fx.
Moved 7 to the right of expression
It becomes -2%2Ax%5E2-5%2Ax%5E%281-2%29-7%2Ax%2Bx-2%2Fx%2B2%2Ax-3%2Fx%2Bhighlight_green%28+7+%29.
Look at .
Added fractions or integers together
It becomes -2%2Ax%5E2-5%2Ax%5E%28highlight_green%28+-1+%29%29-7%2Ax%2Bx-2%2Fx%2B2%2Ax-3%2Fx%2B7.
Look at -2%2Ax%5E2-5%2Ax%5E%28highlight_red%28+-1+%29%29-7%2Ax%2Bx-2%2Fx%2B2%2Ax-3%2Fx%2B7.
Removed extra sign in front of -1
It becomes -2%2Ax%5E2-5%2Ax%5E%28-highlight_green%28+1+%29%29-7%2Ax%2Bx-2%2Fx%2B2%2Ax-3%2Fx%2B7.
Look at .
Eliminated similar terms highlight_red%28+-7%2Ax+%29,highlight_red%28+x+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%28-7%2B1%2B2%29%2Ax+%29
It becomes -2%2Ax%5E2-5%2Ax%5E%28-1%29%2Bhighlight_green%28+%28-7%2B1%2B2%29%2Ax+%29-2%2Fx-3%2Fx%2B7.
Look at .
Eliminated similar terms highlight_red%28+-2%2Fx+%29,highlight_red%28+-3%2Fx+%29 replacing them with highlight_green%28+%28-2-3%29%2Fx+%29
It becomes .
Look at .
Added fractions or integers together
It becomes -2%2Ax%5E2-5%2Ax%5E%28-1%29%2B%28highlight_green%28+-4+%29%29%2Ax%2B%28-2-3%29%2Fx%2B7.
Look at .
Added fractions or integers together
It becomes -2%2Ax%5E2-5%2Ax%5E%28-1%29%2B%28-4%29%2Ax%2B%28highlight_green%28+-5+%29%29%2Fx%2B7.
Look at -2%2Ax%5E2-5%2Ax%5E%28-1%29%2B%28highlight_red%28+-4+%29%29%2Ax%2B%28-5%29%2Fx%2B7.
Removed extra sign in front of -4
It becomes -2%2Ax%5E2-5%2Ax%5E%28-1%29%2B%28-highlight_green%28+4+%29%29%2Ax%2B%28-5%29%2Fx%2B7.
Look at -2%2Ax%5E2-5%2Ax%5E%28-1%29%2B%28-4%29%2Ax%2B%28highlight_red%28+-5+%29%29%2Fx%2B7.
Removed extra sign in front of -5
It becomes -2%2Ax%5E2-5%2Ax%5E%28-1%29%2B%28-4%29%2Ax%2B%28-highlight_green%28+5+%29%29%2Fx%2B7.
Look at .
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes -2%2Ax%5E2-5%2Ax%5E%28-1%29-highlight_green%28+4+%29%2Ax%2B%28-5%29%2Fx%2B7.
Look at .
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes -2%2Ax%5E2-5%2Ax%5E%28-1%29-4%2Ax-highlight_green%28+5+%29%2Fx%2B7.
Look at -2%2Ax%5E2-5%2Ahighlight_red%28+x%5E%28-1%29+%29-4%2Ax-5%2Fx%2B7.
Negative power changes multiplication to division
It becomes -2%2Ax%5E2-5%2Fhighlight_green%28+x%5E1+%29-4%2Ax-5%2Fx%2B7.
Look at -2%2Ax%5E2-5%2Fx%5Ehighlight_red%28+1+%29-4%2Ax-5%2Fx%2B7.
Removing power of one highlight_red%28+1+%29
Look at -2%2Ax%5E2-highlight_red%28+5%2Fx+%29-4%2Ax-highlight_red%28+5%2Fx+%29%2B7.
Eliminated similar terms highlight_red%28+-5%2Fx+%29,highlight_red%28+-5%2Fx+%29 replacing them with highlight_green%28+%28-5-5%29%2Fx+%29
It becomes -2%2Ax%5E2%2Bhighlight_green%28+%28-5-5%29%2Fx+%29-4%2Ax%2B7.
Look at -2%2Ax%5E2%2B%28-highlight_red%28+5+%29-highlight_red%28+5+%29%29%2Fx-4%2Ax%2B7.
Added fractions or integers together
It becomes -2%2Ax%5E2%2B%28highlight_green%28+-10+%29%29%2Fx-4%2Ax%2B7.
Look at -2%2Ax%5E2%2B%28highlight_red%28+-10+%29%29%2Fx-4%2Ax%2B7.
Removed extra sign in front of -10
It becomes -2%2Ax%5E2%2B%28-highlight_green%28+10+%29%29%2Fx-4%2Ax%2B7.
Look at -2%2Ax%5E2%2Bhighlight_red%28+%28-highlight_red%28+10+%29%29%2Fx+%29-4%2Ax%2B7.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes -2%2Ax%5E2-highlight_green%28+10+%29%2Fx-4%2Ax%2B7.
Result: -2%2Ax%5E2-10%2Fx-4%2Ax%2B7

Universal Simplifier and Solver


Done!

Functions/20363: State the domain and range of the function f(x)= x(squared)- 3
1 solutions
Answer 9813 by ichudov(499) About Me  on 2005-11-21 20:54:26 (Show Source):
You can put this solution on YOUR website!
The domain is all the points where this expression x%5E2-3 makes sense. It makes sense for any value of x, so its domain is all real numbers.


Let's graph it to see its graph, that would quickly give you the idea of what it looks like
+graph%28+500%2C+500%2C+-10%2C+10%2C+-5%2C+10%2C+x%5E2-3+%29+
You can see that the smallest value is clearly -3, and there is no biggest value -- any number above 3. That makes its range from -3 to infinity.

Graphs/20360: Help - I'm a mom trying to help my son with his pre-algebra.
The Prentice Hall book says to Graph the equation.
4x + y = -3
We've been able to solve for x
by x + y = -3/4
then x = -3/4 - y
This matches up with the answer in the back of the book - it shows the graph -
but can't figure out how to solve for y.
Any help would be gratefully appreciated.
1 solutions
Answer 9811 by ichudov(499) About Me  on 2005-11-21 20:48:46 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 4+x+%2B+1+y+=+-3 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-4%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -3/4 = -0.75.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -3/1 = -3.
  • Slope is -4/1 = -4.
  • Equation in slope-intercept form: y=-4*x+-3.
graph%28+500%2C+500%2C+-0.75-8%2C+-0.75%2B8%2C+-3-8%2C+-3%2B8%2C+-4%2Ax%2B-3+%29+

Equations/19974: can you please solve this equation 11(4-6y)+5(13y+1)=9
1 solutions
Answer 9619 by ichudov(499) About Me  on 2005-11-17 05:58:59 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: y=40.
  • Graphical form: Equation 11%2A%284-6y%29%2B5%2A%2813y%2B1%29=9 was fully solved.
  • Text form: 11*(4-6y)+5*(13y+1)=9 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+11%2A%284-6y%29%2B5%2A%2813y%2B1%29=9+%29
    For tutors: simplify_cartoon( 11*(4-6y)+5*(13y+1)=9 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 11%2A%28highlight_red%28+4+%29-6%2Ay%29%2B5%2A%2813%2Ay%2B1%29=9.
Moved 4 to the right of expression
It becomes 11%2A%28-6%2Ay%2Bhighlight_green%28+4+%29%29%2B5%2A%2813%2Ay%2B1%29=9.
Look at 11%2A%28-6%2Ay%2B4%29%2B5%2A%2813%2Ay%2B1%29=highlight_red%28+9+%29.
Moved these terms to the left highlight_green%28+-9+%29
It becomes 11%2A%28-6%2Ay%2B4%29%2B5%2A%2813%2Ay%2B1%29-highlight_green%28+9+%29=0.
Look at highlight_red%28+11%2A%28-6%2Ay%2B4%29+%29%2B5%2A%2813%2Ay%2B1%29-9=0.
Expanded term 11 by using associative property on %28-6%2Ay%2B4%29
It becomes .
Look at -highlight_red%28+11+%29%2Ahighlight_red%28+6+%29%2Ay%2B11%2A4%2B5%2A%2813%2Ay%2B1%29-9=0.
Multiplied numerator integers
It becomes -highlight_green%28+66+%29%2Ay%2B11%2A4%2B5%2A%2813%2Ay%2B1%29-9=0.
Look at -66%2Ay%2Bhighlight_red%28+11+%29%2Ahighlight_red%28+4+%29%2B5%2A%2813%2Ay%2B1%29-9=0.
Multiplied numerator integers
It becomes -66%2Ay%2Bhighlight_green%28+44+%29%2B5%2A%2813%2Ay%2B1%29-9=0.
Look at -66%2Ay%2Bhighlight_red%28+44+%29%2B5%2A%2813%2Ay%2B1%29-highlight_red%28+9+%29=0.
Added fractions or integers together
It becomes -66%2Ay%2Bhighlight_green%28+35+%29%2B5%2A%2813%2Ay%2B1%29=0.
Look at -66%2Ay%2Bhighlight_red%28+35+%29%2B5%2A%2813%2Ay%2B1%29=0.
Moved 35 to the right of expression
It becomes -66%2Ay%2B5%2A%2813%2Ay%2B1%29%2Bhighlight_green%28+35+%29=0.
Look at -66%2Ay%2Bhighlight_red%28+5%2A%2813%2Ay%2B1%29+%29%2B35=0.
Expanded term 5 by using associative property on %2813%2Ay%2B1%29
It becomes -66%2Ay%2Bhighlight_green%28+5%2A13%2Ay+%29%2Bhighlight_green%28+5%2A1+%29%2B35=0.
Look at -66%2Ay%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+13+%29%2Ay%2B5%2A1%2B35=0.
Multiplied numerator integers
It becomes -66%2Ay%2Bhighlight_green%28+65+%29%2Ay%2B5%2A1%2B35=0.
Look at -66%2Ay%2B65%2Ay%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+1+%29%2B35=0.
Multiplied numerator integers
It becomes -66%2Ay%2B65%2Ay%2Bhighlight_green%28+5+%29%2B35=0.
Look at -66%2Ay%2B65%2Ay%2Bhighlight_red%28+5+%29%2Bhighlight_red%28+35+%29=0.
Added fractions or integers together
It becomes -66%2Ay%2B65%2Ay%2Bhighlight_green%28+40+%29=0.
Look at -highlight_red%28+66%2Ay+%29%2Bhighlight_red%28+65%2Ay+%29%2B40=0.
Eliminated similar terms highlight_red%28+-66%2Ay+%29,highlight_red%28+65%2Ay+%29 replacing them with highlight_green%28+%28-66%2B65%29%2Ay+%29
It becomes highlight_green%28+%28-66%2B65%29%2Ay+%29%2B40=0.
Look at %28-highlight_red%28+66+%29%2Bhighlight_red%28+65+%29%29%2Ay%2B40=0.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2Ay%2B40=0.
Look at %28highlight_red%28+-1+%29%29%2Ay%2B40=0.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2Ay%2B40=0.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2Ay+%29%2B40=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2Ay%2B40=0.
Look at -highlight_red%28+1+%29%2Ay%2B40=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -y%2B40=0.
Look at highlight_red%28+-y%2B40+%29=0.
Solved linear equation highlight_red%28+-y%2B40=0+%29 equivalent to -y+40 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=40.

Universal Simplifier and Solver


Done!

Expressions-with-variables/10318: simplify 2(x - 5) - 3(4x + 4)
1 solutions
Answer 5501 by ichudov(499) About Me  on 2005-09-09 23:04:45 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 2%2A%28x-5%29-3%2A%284x%2B4%29 simplifies to -10%2Ax-22
  • Text form: 2*(x-5)-3*(4x+4) simplifies to -10*x-22
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%28x-5%29-3%2A%284x%2B4%29+%29
    For tutors: simplify_cartoon( 2*(x-5)-3*(4x+4) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+2%2A%28x-5%29+%29-3%2A%284%2Ax%2B4%29.
Expanded term 2 by using associative property on %28x-5%29
It becomes highlight_green%28+2%2Ax+%29-highlight_green%28+2%2A5+%29-3%2A%284%2Ax%2B4%29.
Look at 2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+5+%29-3%2A%284%2Ax%2B4%29.
Multiplied numerator integers
It becomes 2%2Ax-highlight_green%28+10+%29-3%2A%284%2Ax%2B4%29.
Look at 2%2Ax-highlight_red%28+10+%29-3%2A%284%2Ax%2B4%29.
Moved -10 to the right of expression
It becomes 2%2Ax-3%2A%284%2Ax%2B4%29-highlight_green%28+10+%29.
Look at 2%2Ax-highlight_red%28+3%2A%284%2Ax%2B4%29+%29-10.
Expanded term -3 by using associative property on %284%2Ax%2B4%29
It becomes 2%2Ax-highlight_green%28+3%2A4%2Ax+%29-highlight_green%28+3%2A4+%29-10.
Look at 2%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+4+%29%2Ax-3%2A4-10.
Multiplied numerator integers
It becomes 2%2Ax-highlight_green%28+12+%29%2Ax-3%2A4-10.
Look at 2%2Ax-12%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+4+%29-10.
Multiplied numerator integers
It becomes 2%2Ax-12%2Ax-highlight_green%28+12+%29-10.
Look at 2%2Ax-12%2Ax-highlight_red%28+12+%29-highlight_red%28+10+%29.
Added fractions or integers together
It becomes 2%2Ax-12%2Ax%2Bhighlight_green%28+-22+%29.
Look at 2%2Ax-12%2Ax%2Bhighlight_red%28+-22+%29.
Removed extra sign in front of -22
It becomes 2%2Ax-12%2Ax-highlight_green%28+22+%29.
Look at highlight_red%28+2%2Ax+%29-highlight_red%28+12%2Ax+%29-22.
Eliminated similar terms highlight_red%28+2%2Ax+%29,highlight_red%28+-12%2Ax+%29 replacing them with highlight_green%28+%282-12%29%2Ax+%29
It becomes highlight_green%28+%282-12%29%2Ax+%29-22.
Look at %28highlight_red%28+2+%29-highlight_red%28+12+%29%29%2Ax-22.
Added fractions or integers together
It becomes %28highlight_green%28+-10+%29%29%2Ax-22.
Look at %28highlight_red%28+-10+%29%29%2Ax-22.
Removed extra sign in front of -10
It becomes %28-highlight_green%28+10+%29%29%2Ax-22.
Look at highlight_red%28+%28-highlight_red%28+10+%29%29%2Ax+%29-22.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes -highlight_green%28+10+%29%2Ax-22.
Result: -10%2Ax-22

Universal Simplifier and Solver


Done!


2(x - 5) - 3(4x + 4)
use the distributive property
do 2 times x minus 2 times 5 minus -3 times 4x plus -3 times 4
you do the -3 because the "-" sign makes it negative

2x-10-12x+(-12)
combine like terms
-10x-10+-12
combine like terms
-10x-22

Linear-systems/10334: x = (3x-5)
2 4

I have tried every thing and cant figure it out please help
1 solutions
Answer 5500 by ichudov(499) About Me  on 2005-09-09 23:03:56 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=2.5.
  • Graphical form: Equation x=%283x-5%29 was fully solved.
  • Text form: x=(3x-5) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x=%283x-5%29+%29
    For tutors: simplify_cartoon( x=(3x-5) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x=highlight_red%28+%283%2Ax-5%29+%29.
Remove unneeded parentheses around terms highlight_red%28+3%2Ax+%29,highlight_red%28+-5+%29
It becomes x=highlight_green%28+3%2Ax+%29-highlight_green%28+5+%29.
Look at x=highlight_red%28+3%2Ax-5+%29.
Moved these terms to the left highlight_green%28+-3%2Ax+%29,highlight_green%28+5+%29
It becomes x-highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+5+%29=0.
Look at highlight_red%28+x+%29-highlight_red%28+3%2Ax+%29%2B5=0.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+-3%2Ax+%29 replacing them with highlight_green%28+%281-3%29%2Ax+%29
It becomes highlight_green%28+%281-3%29%2Ax+%29%2B5=0.
Look at %28highlight_red%28+1+%29-highlight_red%28+3+%29%29%2Ax%2B5=0.
Added fractions or integers together
It becomes %28highlight_green%28+-2+%29%29%2Ax%2B5=0.
Look at %28highlight_red%28+-2+%29%29%2Ax%2B5=0.
Removed extra sign in front of -2
It becomes %28-highlight_green%28+2+%29%29%2Ax%2B5=0.
Look at highlight_red%28+%28-highlight_red%28+2+%29%29%2Ax+%29%2B5=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes -highlight_green%28+2+%29%2Ax%2B5=0.
Look at highlight_red%28+-2%2Ax%2B5+%29=0.
Solved linear equation highlight_red%28+-2%2Ax%2B5=0+%29 equivalent to -2*x+5 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=2.5.

Universal Simplifier and Solver


Done!

Inverses/8644: (5c-7)(-3)=
1 solutions
Answer 4972 by ichudov(499) About Me  on 2005-09-01 11:22:32 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: %285c-7%29%2A%28-3%29 simplifies to -15%2Ac%2B21
  • Text form: (5c-7)*(-3) simplifies to -15*c+21
  • Cartoon (animation) form: simplify_cartoon%28+%285c-7%29%2A%28-3%29+%29
    For tutors: simplify_cartoon( (5c-7)*(-3) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%285%2Ac-7%29%2A%28-highlight_red%28+3+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes -%285%2Ac-7%29%2Ahighlight_green%28+3+%29.
Look at -highlight_red%28+%285%2Ac-7%29%2A3+%29.
Expanded term -3 by using associative property on %285%2Ac-7%29
It becomes -highlight_green%28+3%2A5%2Ac+%29%2Bhighlight_green%28+3%2A7+%29.
Look at -highlight_red%28+3+%29%2Ahighlight_red%28+5+%29%2Ac%2B3%2A7.
Multiplied numerator integers
It becomes -highlight_green%28+15+%29%2Ac%2B3%2A7.
Look at -15%2Ac%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+7+%29.
Multiplied numerator integers
It becomes -15%2Ac%2Bhighlight_green%28+21+%29.
Result: -15%2Ac%2B21

Universal Simplifier and Solver


Done!