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Recent problems solved by 'Alwayscheerful'

Alwayscheerful answered: 414 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419, >>Next

Graphs/115308: how do u graph 2x+y=3
1 solutions
Answer 83914 by Alwayscheerful(414) About Me  on 2007-12-07 18:31:43 (Show Source):
You can put this solution on YOUR website!
you first have to change it to slope-intercept form, which is y=mx%2Bb
where m is the slope, and b is the y-intercept
2x%2By=3
y=-2x%2B3
The slope is -2, which means the graph will have a negative slope and 2%2F1
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2x%2B3%29
Hope this helps!

Linear-equations/75565: This question is from textbook
Graph the equations:
x-y=4
1 solutions
Answer 54209 by Alwayscheerful(414) About Me  on 2007-03-22 23:17:57 (Show Source):
You can put this solution on YOUR website!
The easiest way to graph a line is in slope-intercept form. y=mx%2Bb
x-y=4
-y=-x%2B4
multiply by -1 because y must be positive
y=x-4
your slope of the line is 1
y-intercept is -4
The graph would look like:
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2Cx-4%29
Hope this helps!

Linear-equations/75564: This question is from textbook
Graph the equations:
2x+y=5
1 solutions
Answer 54208 by Alwayscheerful(414) About Me  on 2007-03-22 23:16:04 (Show Source):
You can put this solution on YOUR website!
The easiest way to graph a line is with slope-intercept form. y=mx%2Bb
2x%2By=5
y=-2x%2B5
-2 is your slope
5 is your y-intercept
A graph would look like:
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2x%2B5%29
Hope this helps!

Exponents-negative-and-fractional/75517: This question is from textbook algebra
-2.57 exponent 0
1 solutions
Answer 54207 by Alwayscheerful(414) About Me  on 2007-03-22 23:14:27 (Show Source):
You can put this solution on YOUR website!
anything to the exponent of 0 is ALWAYS 1.
Hope this helps!

Polynomials-and-rational-expressions/75553: did i solve this right?
(4m-3n)(4m+3n)
=4m*4m=16m^2
3n*3n=9n^2
=16m^2+n^2
1 solutions
Answer 54206 by Alwayscheerful(414) About Me  on 2007-03-22 23:12:19 (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: %284m-3n%29%2A%284m%2B3n%29 simplifies to 16%2Am%5E2-9%2An%5E2
  • Text form: (4m-3n)*(4m+3n) simplifies to 16*m^2-9*n^2
  • Cartoon (animation) form: simplify_cartoon%28+%284m-3n%29%2A%284m%2B3n%29+%29
    For tutors: simplify_cartoon( (4m-3n)*(4m+3n) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%284%2Am-3%2An%29%2A%284%2Am%2B3%2An%29+%29.
Expanded term %284%2Am%2B3%2An%29 by using associative property on %284%2Am-3%2An%29
It becomes .
Look at highlight_red%28+%284%2Am%2B3%2An%29%2A4%2Am+%29-%284%2Am%2B3%2An%29%2A3%2An.
Expanded term 4%2Am by using associative property on %284%2Am%2B3%2An%29
It becomes .
Look at .
Multiplied numerator integers
It becomes highlight_green%28+16+%29%2Am%2Am%2B4%2Am%2A3%2An-%284%2Am%2B3%2An%29%2A3%2An.
Look at .
Multiplied numerator integers
It becomes 16%2Am%2Am%2Bhighlight_green%28+12+%29%2Am%2An-%284%2Am%2B3%2An%29%2A3%2An.
Look at .
Reduce similar several occurrences of highlight_red%28+m+%29 to highlight_green%28+m%5E2+%29
It becomes 16%2Ahighlight_green%28+m%5E2+%29%2B12%2Am%2An-%284%2Am%2B3%2An%29%2A3%2An.
Look at 16%2Am%5E2%2B12%2Am%2An-highlight_red%28+%284%2Am%2B3%2An%29%2A3%2An+%29.
Expanded term -3%2An by using associative property on %284%2Am%2B3%2An%29
It becomes .
Look at .
Multiplied numerator integers
It becomes 16%2Am%5E2%2B12%2Am%2An-highlight_green%28+12+%29%2An%2Am-3%2An%2A3%2An.
Look at 16%2Am%5E2%2B12%2Am%2An-12%2An%2Am-highlight_red%28+3+%29%2An%2Ahighlight_red%28+3+%29%2An.
Multiplied numerator integers
It becomes 16%2Am%5E2%2B12%2Am%2An-12%2An%2Am-highlight_green%28+9+%29%2An%2An.
Look at 16%2Am%5E2%2B12%2Am%2An-12%2An%2Am-9%2Ahighlight_red%28+n+%29%2Ahighlight_red%28+n+%29.
Reduce similar several occurrences of highlight_red%28+n+%29 to highlight_green%28+n%5E2+%29
It becomes 16%2Am%5E2%2B12%2Am%2An-12%2An%2Am-9%2Ahighlight_green%28+n%5E2+%29.
Look at 16%2Am%5E2%2Bhighlight_red%28+12%2Am%2An+%29-highlight_red%28+12%2An%2Am+%29-9%2An%5E2.
Eliminated similar terms highlight_red%28+12%2Am%2An+%29,highlight_red%28+-12%2An%2Am+%29 replacing them with highlight_green%28+%2812-12%29%2Am%2An+%29
It becomes 16%2Am%5E2%2Bhighlight_green%28+%2812-12%29%2Am%2An+%29-9%2An%5E2.
Look at 16%2Am%5E2%2Bhighlight_red%28+%2812-12%29%2Am%2An+%29-9%2An%5E2.
Since highlight_red%28+%2812-12%29%2Am%2An+%29 has zero as a factor, it should be replaced with a zero
Look at 16%2Am%5E2%2B0-9%2An%5E2.
Added fractions or integers together
It becomes 16%2Am%5E2%2B0-9%2An%5E2.
Look at 16%2Am%5E2%2Bhighlight_red%28+0+%29-9%2An%5E2.
Remove extraneous zero highlight_red%28+0+%29
It becomes 16%2Am%5E2-9%2An%5E2.
Result: 16%2Am%5E2-9%2An%5E2

Universal Simplifier and Solver


Done!

When two terms in parenthesis are adjacent to each other, you need to multiply them, not set them equal to each other.
Hope this helps!

Polynomials-and-rational-expressions/75555: find the value of the polynomial-x^2-10x+6 when x=2
can you please check this for me?
-x^2-10+6
-(-2^2)-10(-2)+6
4+20-6=22
1 solutions
Answer 54205 by Alwayscheerful(414) About Me  on 2007-03-22 23:10:28 (Show Source):
You can put this solution on YOUR website!
Plug 2 everywhere you see "x"
-%282%29%5E2-10%282%29%2B6
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: -%282%29%5E2-10%2A%282%29%2B6 simplifies to -18
  • Text form: -(2)^2-10*(2)+6 simplifies to -18
  • Cartoon (animation) form: simplify_cartoon%28+-%282%29%5E2-10%2A%282%29%2B6+%29
    For tutors: simplify_cartoon( -(2)^2-10*(2)+6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -%282%29%5E2-highlight_red%28+10%2A%28highlight_red%28+2+%29%29+%29%2B6.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes -%282%29%5E2-10%2Ahighlight_green%28+2+%29%2B6.
Look at -highlight_red%28+%282%29+%29%5Ehighlight_red%28+2+%29-10%2A2%2B6.
Replace constants in factor: highlight_red%28+%282%29+%29,highlight_red%28+2+%29 with highlight_green%28+4+%29
It becomes -highlight_green%28+4+%29-10%2A2%2B6.
Look at -4-highlight_red%28+10+%29%2Ahighlight_red%28+2+%29%2B6.
Multiplied numerator integers
It becomes -4-highlight_green%28+20+%29%2B6.
Look at -highlight_red%28+4+%29-highlight_red%28+20+%29%2Bhighlight_red%28+6+%29.
Added fractions or integers together
It becomes highlight_green%28+-18+%29.
Look at highlight_red%28+-18+%29.
Removed extra sign in front of -18
It becomes -highlight_green%28+18+%29.
Result: -18

Universal Simplifier and Solver


Done!

Your answer was close, but what you did wrong was you plugged in -2 in for x in the first term, while x is 2.
Hope this helps!

Linear-systems/75064: How would you graph y=2x+2?
1 solutions
Answer 53913 by Alwayscheerful(414) About Me  on 2007-03-19 23:27:10 (Show Source):
You can put this solution on YOUR website!
In slope intercept form (y=mx+b), "m" is the slope of the line, and "b" is the y-intercept.

In your case, the slope is 2 and the y-intercept is also 2.
The graph of the line would look like this:
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C2x%2B2%29
Hope this helps!

Quadratic_Equations/75015: This question is from textbook Algebra 1
y-5=1/3(x+2)^2 (Thank - you)
1 solutions
Answer 53912 by Alwayscheerful(414) About Me  on 2007-03-19 23:24:08 (Show Source):
You can put this solution on YOUR website!
From your graph equation, you know the vertex of your parabola.
(-2,5) - vertex
And since the "a" value of the equation is positive, you know that your graph will open up.
To get more points, plug in a point for "x" and you'll get a "y" value.
Graph:
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C%281%2F3%29x%5E2%2B%284%2F3%29x%2B%2819%2F3%29%29
Hope this helps!

Exponential-and-logarithmic-functions/74893: Could you please help me to simplify this problem:
2^(2/3) + 3(2^(2/3).
1 solutions
Answer 53833 by Alwayscheerful(414) About Me  on 2007-03-18 23:07:12 (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%5E%282%2F3%29%2B3%2A%282%5E%282%2F3%29%29 simplifies to 6.3496042078728
  • Text form: 2^(2/3)+3*(2^(2/3)) simplifies to 6.3496042078728
  • Cartoon (animation) form: simplify_cartoon%28+2%5E%282%2F3%29%2B3%2A%282%5E%282%2F3%29%29+%29
    For tutors: simplify_cartoon( 2^(2/3)+3*(2^(2/3)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%5E%282%2F3%29%2Bhighlight_red%28+3%2A%28highlight_red%28+2%5E%282%2F3%29+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+2%5E%282%2F3%29+%29
It becomes 2%5E%282%2F3%29%2B3%2Ahighlight_green%28+2%5E%282%2F3%29+%29.
Look at highlight_red%28+2+%29%5Ehighlight_red%28+%282%2F3%29+%29%2B3%2A2%5E%282%2F3%29.
Replace constants in factor: highlight_red%28+2+%29,highlight_red%28+%282%2F3%29+%29 with highlight_green%28+1.5874010519682+%29
It becomes highlight_green%28+1.5874010519682+%29%2B3%2A2%5E%282%2F3%29.
Look at 1.5874010519682%2B3%2Ahighlight_red%28+2+%29%5Ehighlight_red%28+%282%2F3%29+%29.
Replace constants in factor: highlight_red%28+2+%29,highlight_red%28+%282%2F3%29+%29 with highlight_green%28+1.5874010519682+%29
It becomes 1.5874010519682%2B3%2Ahighlight_green%28+1.5874010519682+%29.
Look at highlight_red%28+1.5874010519682+%29%2Bhighlight_red%28+3%2A1.5874010519682+%29.
Replace constants in expression: highlight_red%28+1.5874010519682+%29,highlight_red%28+3%2A1.5874010519682+%29 with highlight_green%28+6.3496042078728+%29
It becomes highlight_green%28+6.3496042078728+%29.
Result: 6.3496042078728

Universal Simplifier and Solver


Done!

Hope this helps!

Numeric_Fractions/74912: what is the perimeter of a 4 cm multiply 2 cm rectangle
1 solutions
Answer 53832 by Alwayscheerful(414) About Me  on 2007-03-18 23:04:50 (Show Source):
You can put this solution on YOUR website!
A perimeter is defined as the sum of all the sides of the rectangle. So in your case, it would be 4%2B2%2B4%2B2=12cm
Hope this helps!

Linear-systems/74917: Find the eqiuation of the line with x-intercept 12 ,and y-intercept 4
1 solutions
Answer 53830 by Alwayscheerful(414) About Me  on 2007-03-18 22:58:05 (Show Source):
You can put this solution on YOUR website!
The x-intercept can be written as point (12,0) and the y-intercept can be written as (0,4).
If you use the slope-intercept form for a line (y=mx%2Bb), then you must find m, which is the slope, and b, which is the y-intercept.
To find m, use the formula %28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29.
Plug the points in:
%280-4%29%2F%2812-0%29=-1%2F3
Now that you have the value of m and you have the value of b given to you in the question (4), you can plug the numbers into the slope-intercept formula for the equation of your line.
y=-%281%2F3%29x%2B4
That line graphed would look like:
graph%28500%2C500%2C-15%2C15%2C-15%2C15%2C-%281%2F3%29x%2B4%29
Hope this helps!

Equations/37909: 2x-9 = 8-3x
1 solutions
Answer 24028 by Alwayscheerful(414) About Me  on 2006-05-19 00:06:39 (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=3.4.
  • Graphical form: Equation 2x-9=8-3x was fully solved.
  • Text form: 2x-9=8-3x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2x-9=8-3x+%29
    For tutors: simplify_cartoon( 2x-9=8-3x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2Ax-9=highlight_red%28+8+%29-3%2Ax.
Moved 8 to the right of expression
It becomes 2%2Ax-9=-3%2Ax%2Bhighlight_green%28+8+%29.
Look at 2%2Ax-9=highlight_red%28+-3%2Ax%2B8+%29.
Moved these terms to the left highlight_green%28+3%2Ax+%29,highlight_green%28+-8+%29
It becomes 2%2Ax-9%2Bhighlight_green%28+3%2Ax+%29-highlight_green%28+8+%29=0.
Look at 2%2Ax-highlight_red%28+9+%29%2B3%2Ax-highlight_red%28+8+%29=0.
Added fractions or integers together
It becomes 2%2Ax%2Bhighlight_green%28+-17+%29%2B3%2Ax=0.
Look at 2%2Ax%2Bhighlight_red%28+-17+%29%2B3%2Ax=0.
Moved -17 to the right of expression
It becomes 2%2Ax%2B3%2Ax%2Bhighlight_green%28+-17+%29=0.
Look at 2%2Ax%2B3%2Ax%2Bhighlight_red%28+-17+%29=0.
Removed extra sign in front of -17
It becomes 2%2Ax%2B3%2Ax-highlight_green%28+17+%29=0.
Look at highlight_red%28+2%2Ax+%29%2Bhighlight_red%28+3%2Ax+%29-17=0.
Eliminated similar terms highlight_red%28+2%2Ax+%29,highlight_red%28+3%2Ax+%29 replacing them with highlight_green%28+%282%2B3%29%2Ax+%29
It becomes highlight_green%28+%282%2B3%29%2Ax+%29-17=0.
Look at %28highlight_red%28+2+%29%2Bhighlight_red%28+3+%29%29%2Ax-17=0.
Added fractions or integers together
It becomes %28highlight_green%28+5+%29%29%2Ax-17=0.
Look at highlight_red%28+%28highlight_red%28+5+%29%29%2Ax+%29-17=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes highlight_green%28+5+%29%2Ax-17=0.
Look at highlight_red%28+5%2Ax-17+%29=0.
Solved linear equation highlight_red%28+5%2Ax-17=0+%29 equivalent to 5*x-17 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=3.4.

Universal Simplifier and Solver


Done!

Hope this helps!

Geometry_Word_Problems/38460: This question is from textbook
x= 2y-1 and 2x+y=81
solve using substitution
x=?
y=?
show work please thank you!!
1 solutions
Answer 24026 by Alwayscheerful(414) About Me  on 2006-05-18 23:53:27 (Show Source):
You can put this solution on YOUR website!
First step, plug x into the values of x
x=+2y-1
2%282y-1%29%2By=81
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: y=16.6.
  • Graphical form: Equation 2%2A%282y-1%29%2By=81 was fully solved.
  • Text form: 2*(2y-1)+y=81 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%282y-1%29%2By=81+%29
    For tutors: simplify_cartoon( 2*(2y-1)+y=81 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%282%2Ay-1%29%2By=highlight_red%28+81+%29.
Moved these terms to the left highlight_green%28+-81+%29
It becomes 2%2A%282%2Ay-1%29%2By-highlight_green%28+81+%29=0.
Look at highlight_red%28+2%2A%282%2Ay-1%29+%29%2By-81=0.
Expanded term 2 by using associative property on %282%2Ay-1%29
It becomes highlight_green%28+2%2A2%2Ay+%29-highlight_green%28+2%2A1+%29%2By-81=0.
Look at highlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2Ay-2%2A1%2By-81=0.
Multiplied numerator integers
It becomes highlight_green%28+4+%29%2Ay-2%2A1%2By-81=0.
Look at 4%2Ay-highlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2By-81=0.
Multiplied numerator integers
It becomes 4%2Ay-highlight_green%28+2+%29%2By-81=0.
Look at 4%2Ay-highlight_red%28+2+%29%2By-highlight_red%28+81+%29=0.
Added fractions or integers together
It becomes 4%2Ay%2Bhighlight_green%28+-83+%29%2By=0.
Look at 4%2Ay%2Bhighlight_red%28+-83+%29%2By=0.
Moved -83 to the right of expression
It becomes 4%2Ay%2By%2Bhighlight_green%28+-83+%29=0.
Look at 4%2Ay%2By%2Bhighlight_red%28+-83+%29=0.
Removed extra sign in front of -83
It becomes 4%2Ay%2By-highlight_green%28+83+%29=0.
Look at highlight_red%28+4%2Ay+%29%2Bhighlight_red%28+y+%29-83=0.
Eliminated similar terms highlight_red%28+4%2Ay+%29,highlight_red%28+y+%29 replacing them with highlight_green%28+%284%2B1%29%2Ay+%29
It becomes highlight_green%28+%284%2B1%29%2Ay+%29-83=0.
Look at %28highlight_red%28+4+%29%2Bhighlight_red%28+1+%29%29%2Ay-83=0.
Added fractions or integers together
It becomes %28highlight_green%28+5+%29%29%2Ay-83=0.
Look at highlight_red%28+%28highlight_red%28+5+%29%29%2Ay+%29-83=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes highlight_green%28+5+%29%2Ay-83=0.
Look at highlight_red%28+5%2Ay-83+%29=0.
Solved linear equation highlight_red%28+5%2Ay-83=0+%29 equivalent to 5*y-83 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=16.6.

Universal Simplifier and Solver


Done!


y=highlight%2816.6%29
Plug y into the equation to find x
x=+2y-1
x=2%2816.6%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=32.2.
  • Graphical form: Equation x=2%2A%2816.6%29-1 was fully solved.
  • Text form: x=2*(16.6)-1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x=2%2A%2816.6%29-1+%29
    For tutors: simplify_cartoon( x=2*(16.6)-1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x=highlight_red%28+2%2A%28highlight_red%28+16.6+%29%29+%29-1.
Remove unneeded parentheses around factor highlight_red%28+16.6+%29
It becomes x=2%2Ahighlight_green%28+16.6+%29-1.
Look at x=highlight_red%28+2%2A16.6+%29-highlight_red%28+1+%29.
Replace constants in expression: highlight_red%28+2%2A16.6+%29,highlight_red%28+-1+%29 with highlight_green%28+32.2+%29
It becomes x=highlight_green%28+32.2+%29.
Look at x=highlight_red%28+32.2+%29.
Moved these terms to the left highlight_green%28+-32.2+%29
It becomes x-highlight_green%28+32.2+%29=0.
Look at highlight_red%28+x-32.2+%29=0.
Solved linear equation highlight_red%28+x-32.2=0+%29 equivalent to x-32.2 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=32.2.

Universal Simplifier and Solver


Done!


x=highlight%2832.2%29
If you need more detailed explanations, you can see the lesson I wrote on substitution.
Hope this helps!

Radicals/38515: Simplify the following radical expressions. Show all work!
I dont understand the method to use to solve the problem.
(squareroot 7+5)squared
1 solutions
Answer 24023 by Alwayscheerful(414) About Me  on 2006-05-18 23:42:58 (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: %28sqrt%287%2B5%29%29%5E2 simplifies to 12
  • Text form: (sqrt(7+5))^2 simplifies to 12
  • Cartoon (animation) form: simplify_cartoon%28+%28sqrt%287%2B5%29%29%5E2+%29
    For tutors: simplify_cartoon( (sqrt(7+5))^2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %28sqrt%28highlight_red%28+7+%29%2Bhighlight_red%28+5+%29%29%29%5E2.
Added fractions or integers together
It becomes %28sqrt%28highlight_green%28+12+%29%29%29%5E2.
Look at highlight_red%28+%28sqrt%2812%29%29+%29%5Ehighlight_red%28+2+%29.
Replace constants in factor: highlight_red%28+%28sqrt%2812%29%29+%29,highlight_red%28+2+%29 with highlight_green%28+12+%29
It becomes highlight_green%28+12+%29.
Result: 12

Universal Simplifier and Solver


Done!

Hope this helps!

Equations/38469: I'm having trouble solving the following problem:
n divided by 4 times 19 +11 = 87
1 solutions
Answer 24022 by Alwayscheerful(414) About Me  on 2006-05-18 23:41:01 (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: n=16.
  • Graphical form: Equation %28n%2F4%29%2A19%2B11=87 was fully solved.
  • Text form: (n/4)*19+11=87 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28n%2F4%29%2A19%2B11=87+%29
    For tutors: simplify_cartoon( (n/4)*19+11=87 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+n%2F4+%29%29%2A19+%29%2B11=87.
Remove unneeded parentheses around factor highlight_red%28+n+%29,highlight_red%28+1%2F4+%29
It becomes highlight_green%28+n+%29%2Fhighlight_green%28+4+%29%2A19%2B11=87.
Look at n%2F4%2A19%2B11=highlight_red%28+87+%29.
Moved these terms to the left highlight_green%28+-87+%29
It becomes n%2F4%2A19%2B11-highlight_green%28+87+%29=0.
Look at n%2F4%2A19%2Bhighlight_red%28+11+%29-highlight_red%28+87+%29=0.
Added fractions or integers together
It becomes n%2F4%2A19%2Bhighlight_green%28+-76+%29=0.
Look at n%2F4%2A19%2Bhighlight_red%28+-76+%29=0.
Removed extra sign in front of -76
It becomes n%2F4%2A19-highlight_green%28+76+%29=0.
Look at highlight_red%28+n%2F4%2A19-76+%29=0.
Solved linear equation highlight_red%28+n%2F4%2A19-76=0+%29 equivalent to 4.75*n-76 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=16.

Universal Simplifier and Solver


Done!

Hope this helps!

Polynomials-and-rational-expressions/38527: This question is from textbook
(3y+2)(y+3)=y+14
1 solutions
Answer 24021 by Alwayscheerful(414) About Me  on 2006-05-18 23:39:00 (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: y=0.666666666666667,y=-4.
  • Graphical form: Equation %283y%2B2%29%2A%28y%2B3%29=y%2B14 was fully solved.
  • Text form: (3y+2)*(y+3)=y+14 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%283y%2B2%29%2A%28y%2B3%29=y%2B14+%29
    For tutors: simplify_cartoon( (3y+2)*(y+3)=y+14 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %283%2Ay%2B2%29%2A%28y%2B3%29=highlight_red%28+y%2B14+%29.
Moved these terms to the left highlight_green%28+-y+%29,highlight_green%28+-14+%29
It becomes %283%2Ay%2B2%29%2A%28y%2B3%29-highlight_green%28+y+%29-highlight_green%28+14+%29=0.
Look at highlight_red%28+%283%2Ay%2B2%29%2A%28y%2B3%29+%29-y-14=0.
Expanded term %28y%2B3%29 by using associative property on %283%2Ay%2B2%29
It becomes highlight_green%28+%28y%2B3%29%2A3%2Ay+%29%2Bhighlight_green%28+%28y%2B3%29%2A2+%29-y-14=0.
Look at highlight_red%28+%28y%2B3%29%2A3%2Ay+%29%2B%28y%2B3%29%2A2-y-14=0.
Expanded term 3%2Ay by using associative property on %28y%2B3%29
It becomes highlight_green%28+3%2Ay%2Ay+%29%2Bhighlight_green%28+3%2Ay%2A3+%29%2B%28y%2B3%29%2A2-y-14=0.
Look at 3%2Ay%2Ay%2Bhighlight_red%28+3+%29%2Ay%2Ahighlight_red%28+3+%29%2B%28y%2B3%29%2A2-y-14=0.
Multiplied numerator integers
It becomes 3%2Ay%2Ay%2Bhighlight_green%28+9+%29%2Ay%2B%28y%2B3%29%2A2-y-14=0.
Look at 3%2Ahighlight_red%28+y+%29%2Ahighlight_red%28+y+%29%2B9%2Ay%2B%28y%2B3%29%2A2-y-14=0.
Reduce similar several occurrences of highlight_red%28+y+%29 to highlight_green%28+y%5E2+%29
It becomes 3%2Ahighlight_green%28+y%5E2+%29%2B9%2Ay%2B%28y%2B3%29%2A2-y-14=0.
Look at 3%2Ay%5E2%2Bhighlight_red%28+9%2Ay+%29%2B%28y%2B3%29%2A2-highlight_red%28+y+%29-14=0.
Eliminated similar terms highlight_red%28+9%2Ay+%29,highlight_red%28+-y+%29 replacing them with highlight_green%28+%289-1%29%2Ay+%29
It becomes 3%2Ay%5E2%2Bhighlight_green%28+%289-1%29%2Ay+%29%2B%28y%2B3%29%2A2-14=0.
Look at 3%2Ay%5E2%2B%28highlight_red%28+9+%29-highlight_red%28+1+%29%29%2Ay%2B%28y%2B3%29%2A2-14=0.
Added fractions or integers together
It becomes 3%2Ay%5E2%2B%28highlight_green%28+8+%29%29%2Ay%2B%28y%2B3%29%2A2-14=0.
Look at 3%2Ay%5E2%2Bhighlight_red%28+%28highlight_red%28+8+%29%29%2Ay+%29%2B%28y%2B3%29%2A2-14=0.
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes 3%2Ay%5E2%2Bhighlight_green%28+8+%29%2Ay%2B%28y%2B3%29%2A2-14=0.
Look at 3%2Ay%5E2%2B8%2Ay%2Bhighlight_red%28+%28y%2B3%29%2A2+%29-14=0.
Expanded term 2 by using associative property on %28y%2B3%29
It becomes 3%2Ay%5E2%2B8%2Ay%2Bhighlight_green%28+2%2Ay+%29%2Bhighlight_green%28+2%2A3+%29-14=0.
Look at 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+3+%29-14=0.
Multiplied numerator integers
It becomes 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_green%28+6+%29-14=0.
Look at 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+6+%29-highlight_red%28+14+%29=0.
Added fractions or integers together
It becomes 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_green%28+-8+%29=0.
Look at 3%2Ay%5E2%2B8%2Ay%2B2%2Ay%2Bhighlight_red%28+-8+%29=0.
Removed extra sign in front of -8
It becomes 3%2Ay%5E2%2B8%2Ay%2B2%2Ay-highlight_green%28+8+%29=0.
Look at 3%2Ay%5E2%2Bhighlight_red%28+8%2Ay+%29%2Bhighlight_red%28+2%2Ay+%29-8=0.
Eliminated similar terms highlight_red%28+8%2Ay+%29,highlight_red%28+2%2Ay+%29 replacing them with highlight_green%28+%288%2B2%29%2Ay+%29
It becomes 3%2Ay%5E2%2Bhighlight_green%28+%288%2B2%29%2Ay+%29-8=0.
Look at 3%2Ay%5E2%2B%28highlight_red%28+8+%29%2Bhighlight_red%28+2+%29%29%2Ay-8=0.
Added fractions or integers together
It becomes 3%2Ay%5E2%2B%28highlight_green%28+10+%29%29%2Ay-8=0.
Look at 3%2Ay%5E2%2Bhighlight_red%28+%28highlight_red%28+10+%29%29%2Ay+%29-8=0.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes 3%2Ay%5E2%2Bhighlight_green%28+10+%29%2Ay-8=0.
Look at highlight_red%28+3%2Ay%5E2%2B10%2Ay-8+%29=0.
Equation highlight_red%28+3%2Ay%5E2%2B10%2Ay-8=0+%29 is a quadratic equation: 3*y^2+10*y-8 =0, and has solutions 0.666666666666667,-4
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=0.666666666666667,y=-4.

Universal Simplifier and Solver


Done!

Hope this helps!

Graphs/38468: Evaluate
5 times 4 divided by 2 - 4^2
1 solutions
Answer 24020 by Alwayscheerful(414) About Me  on 2006-05-18 23:28:34 (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: %285%2A4%29%2F%282-4%5E2%29 simplifies to -1.42857142857143
  • Text form: (5*4)/(2-4^2) simplifies to -1.42857142857143
  • Cartoon (animation) form: simplify_cartoon%28+%285%2A4%29%2F%282-4%5E2%29+%29
    For tutors: simplify_cartoon( (5*4)/(2-4^2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+5%2A4+%29%29%2F%282-4%5E2%29+%29.
Remove unneeded parentheses around factor highlight_red%28+5+%29,highlight_red%28+4+%29
It becomes highlight_green%28+5+%29%2Ahighlight_green%28+4+%29%2F%282-4%5E2%29.
Look at highlight_red%28+5+%29%2Ahighlight_red%28+4+%29%2F%282-4%5E2%29.
Multiplied numerator integers
It becomes highlight_green%28+20+%29%2F%282-4%5E2%29.
Look at highlight_red%28+20%2F%282-4%5E2%29+%29.
Removed extra sign in front of -1.42857142857143
It becomes -highlight_green%28+1.42857142857143+%29.
Result: -1.42857142857143

Universal Simplifier and Solver


Done!

In fraction form, it is 10%2F-7
Hope this helps!

Divisibility_and_Prime_Numbers/38526: How do you write the number in expanded form:

30,672
1 solutions
Answer 24018 by Alwayscheerful(414) About Me  on 2006-05-18 23:24:52 (Show Source):
You can put this solution on YOUR website!
Just separate it number by number.
30,000+600+70+2
Hope this helps!

Graphs/38470: multiply n^10 times n^8
1 solutions
Answer 24017 by Alwayscheerful(414) About Me  on 2006-05-18 23:23:50 (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: n%5E10%2An%5E8 simplifies to n%5E%2818%29
  • Text form: n^10*n^8 simplifies to n^(18)
  • Cartoon (animation) form: simplify_cartoon%28+n%5E10%2An%5E8+%29
    For tutors: simplify_cartoon( n^10*n^8 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+n%5E10+%29%2Ahighlight_red%28+n%5E8+%29.
Reduce similar several occurrences of highlight_red%28+n%5E10+%29 to highlight_green%28+n%5E%2810%2B8%29+%29
It becomes highlight_green%28+n%5E%2810%2B8%29+%29.
Look at n%5E%28highlight_red%28+10+%29%2Bhighlight_red%28+8+%29%29.
Added fractions or integers together
It becomes n%5E%28highlight_green%28+18+%29%29.
Result: n%5E%2818%29

Universal Simplifier and Solver


Done!

Hope this helps!

Equations/38483: This question is from textbook Mathematics Concepts and Skills
How do you solve the equation 9z+z-3=17
1 solutions
Answer 24016 by Alwayscheerful(414) About Me  on 2006-05-18 23:22:12 (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: z=2.
  • Graphical form: Equation 9z%2Bz-3=17 was fully solved.
  • Text form: 9z+z-3=17 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+9z%2Bz-3=17+%29
    For tutors: simplify_cartoon( 9z+z-3=17 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+9%2Az+%29%2Bhighlight_red%28+z+%29-3=17.
Eliminated similar terms highlight_red%28+9%2Az+%29,highlight_red%28+z+%29 replacing them with highlight_green%28+%289%2B1%29%2Az+%29
It becomes highlight_green%28+%289%2B1%29%2Az+%29-3=17.
Look at %28highlight_red%28+9+%29%2Bhighlight_red%28+1+%29%29%2Az-3=17.
Added fractions or integers together
It becomes %28highlight_green%28+10+%29%29%2Az-3=17.
Look at highlight_red%28+%28highlight_red%28+10+%29%29%2Az+%29-3=17.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes highlight_green%28+10+%29%2Az-3=17.
Look at 10%2Az-3=highlight_red%28+17+%29.
Moved these terms to the left highlight_green%28+-17+%29
It becomes 10%2Az-3-highlight_green%28+17+%29=0.
Look at 10%2Az-highlight_red%28+3+%29-highlight_red%28+17+%29=0.
Added fractions or integers together
It becomes 10%2Az%2Bhighlight_green%28+-20+%29=0.
Look at 10%2Az%2Bhighlight_red%28+-20+%29=0.
Removed extra sign in front of -20
It becomes 10%2Az-highlight_green%28+20+%29=0.
Look at highlight_red%28+10%2Az-20+%29=0.
Solved linear equation highlight_red%28+10%2Az-20=0+%29 equivalent to 10*z-20 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: z=2.

Universal Simplifier and Solver


Done!

Hope this helps!

Exponential-and-logarithmic-functions/37955: This question is from textbook Algebra II
1/2(16)3/4
1 solutions
Answer 23460 by Alwayscheerful(414) About Me  on 2006-05-15 20:14:22 (Show Source):
You can put this solution on YOUR website!
It would be extremely helpful if I knew what the question is. So, I'm just going to assume it's a simplification problem.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 1%2F2%2A%2816%29%2A3%2F4 simplifies to 6
  • Text form: 1/2*(16)*3/4 simplifies to 6
  • Cartoon (animation) form: simplify_cartoon%28+1%2F2%2A%2816%29%2A3%2F4+%29
    For tutors: simplify_cartoon( 1/2*(16)*3/4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+1%2F2%2A%28highlight_red%28+16+%29%29%2A3%2F4+%29.
Remove unneeded parentheses around factor highlight_red%28+16+%29
It becomes 1%2F2%2Ahighlight_green%28+16+%29%2A3%2F4.
Look at 1%2Fhighlight_red%28+2+%29%2Ahighlight_red%28+16+%29%2A3%2F4.
Factors 16 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+8+%29%2A3%2F4.
Look at 1%2F1%2Ahighlight_red%28+8+%29%2A3%2Fhighlight_red%28+4+%29.
Factors 8 and 4 have greatest common factor (GCF) of 4. Reducing fraction.
It becomes 1%2F1%2Ahighlight_green%28+2+%29%2A3%2Fhighlight_green%28+1+%29.
Look at highlight_red%28+1+%29%2F1%2Ahighlight_red%28+2+%29%2Ahighlight_red%28+3+%29%2F1.
Multiplied numerator integers
It becomes highlight_green%28+6+%29%2F1%2F1.
Look at 6%2Fhighlight_red%28+1+%29%2Fhighlight_red%28+1+%29.
Multiplied denominator integers
It becomes 6%2Fhighlight_green%28+1+%29.
Look at 6%2Fhighlight_red%28+1+%29.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 6.
Result: 6

Universal Simplifier and Solver


Done!


In the future, type out the whole problem.
Hope this helps!

Geometry_Word_Problems/37957: This question is from textbook
the edge of each cube is 3 inches. if each cube weighs 2.5 ounces per cubic inch. how many pounds will 200 cubes weigh?
thank you id appreciate it alot!!
1 solutions
Answer 23459 by Alwayscheerful(414) About Me  on 2006-05-15 20:12:08 (Show Source):
You can put this solution on YOUR website!
Well think about it.
If 1 cube weighs 2.5 ounces, how many will 2 weigh?
5 ounces of course!
How did I get that? Since there are 2 cubes I just simply multiplied the mass by 2.
So, apply it to the current problem.
How heavy will 200 cubes weigh?
2.5%2A200
Answer: highlight%28500+pounds%29
Hope this helps!

Linear-equations/37923: Graph the line with slope 5 passing through the point(3,-2 .
1 solutions
Answer 23443 by Alwayscheerful(414) About Me  on 2006-05-15 18:48:08 (Show Source):
You can put this solution on YOUR website!
Since the slope is 5, m will be 5%2F1
You have a point, so plug that into slope-intercept form, which is y=mx%2Bb

-2=5%283%29%2Bb
-2=15%2Bb
-17=b
We did that to find the y-intercept.
The equation for your line is y=5x-17
Now just graph it.
graph%28500%2C500%2C-20%2C20%2C-20%2C20%2C5x-17%29
Hope this helps!

Graphs/37918: What is the x intercept in the following equation.
3x + 5y = 30
1 solutions
Answer 23441 by Alwayscheerful(414) About Me  on 2006-05-15 18:40:47 (Show Source):
You can put this solution on YOUR website!
A x-intercept is when y=0.
There are two ways you can do this.
First way:
Set y=0 in your equation
3x%2B5%280%29=30
3x=30
x=10
Second way:
Graph it and see where it crosses the x-axis
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-3%2F5%29x%2B6%29
Both ways, you end with (10,0).
Hope this helps!

Graphs/37920: Graph the line with equation
y= -x-5
1 solutions
Answer 23440 by Alwayscheerful(414) About Me  on 2006-05-15 18:37:54 (Show Source):
You can put this solution on YOUR website!
The standard form for a linear equation is y=mx%2Bb
m represents the slope, rise%2Frun
b represents the y-intercept, when x=0
Plot the y-intercept, then plot more points based on the slope.
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-x-5%29
Hope this helps!

Graphs/37860: This question is from textbook
How do you solve an system by graphing. I see the problem x+y=-5 and-2x+y=1 now I need to figure out how to graph the problem so I can come up with the solution. Thank you!
1 solutions
Answer 23437 by Alwayscheerful(414) About Me  on 2006-05-15 18:24:38 (Show Source):
You can put this solution on YOUR website!
Okay, the easiest way to graph linear lines is to put them in slope-intercept form, which is y=mx%2Bb
m represents the slope, rise%2Frun
b represents the y-intercept, when x=0
x%2By=-5
highlight%28y=-x-5%29

-2x%2By=1
highlight%28y=2x%2B1%29

Now, you have two lines, draw them into your graph.
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-x-5%2C2x%2B1%29
The answer to your system of equations is where the two lines meet.
Answer: (-2,-3)
Hope this helps!

real-numbers/37914: A total of 691 tickets were sold for the school play. There were 59 fewer student tickets sold than adult tickets. How many adult tickets were sold?
1 solutions
Answer 23435 by Alwayscheerful(414) About Me  on 2006-05-15 18:19:07 (Show Source):
You can put this solution on YOUR website!
Let's assign variables to the different groups so we can later solve this system with either substitution or elimination.
Student tickets = s
adult tickets = a
So, translate the english into math.
Since a total of 691 tickets were sold, we can derive the equation:
s%2Ba=691
Then, there were 59 fewer students sold, that means more adult tickets were sold.
s=a-59
Now put these in a system of equations and solve.
s%2Ba=691
s=a-59
For this system, I would suggest substitution because there is already an isolated variable.
%28a-59%29%2Ba=691
2a-59=691
2a=750
a=375
We now know that highlight%28375%29 adult tickets were sold.
s=375-59
s=316
highlight%28316%29 student tickets were sold.
Hope this helps!

Quadratic-relations-and-conic-sections/37900: Hello. I need help with the following problem:
Write the equation of the parabola: y=4x^2-8x+1
Thank you.
1 solutions
Answer 23432 by Alwayscheerful(414) About Me  on 2006-05-15 18:12:53 (Show Source):
You can put this solution on YOUR website!
Don't know if you typed your question wrong, but the equation of the parabola is indeed y=4x%5E2-8x%2B1
This might help.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-8x%2B1+=+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=%28-8%29%5E2-4%2A4%2A1=48.

Discriminant d=48 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+48+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+48+%29%29%2F2%5C4+=+1.86602540378444
x%5B2%5D+=+%28-%28-8%29-sqrt%28+48+%29%29%2F2%5C4+=+0.133974596215561

Quadratic expression 4x%5E2%2B-8x%2B1 can be factored:
4x%5E2%2B-8x%2B1+=+4%28x-1.86602540378444%29%2A%28x-0.133974596215561%29
Again, the answer is: 1.86602540378444, 0.133974596215561. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-8%2Ax%2B1+%29


Hope this helps!

Permutations/37905: What is the difference between permutations and Combinations?
1 solutions
Answer 23431 by Alwayscheerful(414) About Me  on 2006-05-15 18:09:45 (Show Source):
You can put this solution on YOUR website!
The equation for permutations is nPr=n%21%2F%28n-r%29%21
Permutations (compared to combinations) will give you a larger number, which means more combinations.
One example when you use permutations is this:
Say you have 5 chairs lined up in a row. There are 7 kids. How many combinations of kids are there?
You would use permuations because the order of the seating arrangement matters.
Tom, Jerry, Ralph, Jim, and Tony as a group will be different than Jerry, Tom, Jim, Tony, and Ralph.
The equation for combinations is nCr=n%21%2F%28%28n-r%29%21%2Ar%21%29
One common example when you use combinations is when you are electing people to be on a commitee.
Say there are 10 kids running for 3 spots. How many different committees can there be?
For this, the order doesn't matter, because a committee of Tom, Jerry, and Ralph will be the same as a committee of Jerry, Ralph, and Tom.

If the order of the group matters, use permuations. If the order of the group doesn't matter, use combinations.
Hope this helps!

Functions/37791: Find the domain of the rational function.
2
_____
x + 3
Help please?
Thank you


1 solutions
Answer 23326 by Alwayscheerful(414) About Me  on 2006-05-14 23:12:37 (Show Source):
You can put this solution on YOUR website!
The domain of a function is the values of x
If the denominator is zero, the function will be undefined.
So in this case, the domain can't equal zero, so x cannot be -3.
Every other number works in this function except -3.
So, we can say that the domain of this function is "all read numbers except -3".
Hope this helps!

Equations/37798: -9x+15=-22-4(x+12)
-9x+15=-22-4x+48
-9x+15=4x+26
15=5x+26
-11=5x
-2.2=x
1 solutions
Answer 23325 by Alwayscheerful(414) About Me  on 2006-05-14 23:09:10 (Show Source):
You can put this solution on YOUR website!
I'm assuming the steps there is your attempt at the problem
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=17.
  • Graphical form: Equation -9x%2B15=-22-4%2A%28x%2B12%29 was fully solved.
  • Text form: -9x+15=-22-4*(x+12) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-9x%2B15=-22-4%2A%28x%2B12%29+%29
    For tutors: simplify_cartoon( -9x+15=-22-4*(x+12) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -9%2Ax%2B15=-highlight_red%28+22+%29-4%2A%28x%2B12%29.
Moved -22 to the right of expression
It becomes -9%2Ax%2B15=-4%2A%28x%2B12%29-highlight_green%28+22+%29.
Look at -9%2Ax%2B15=highlight_red%28+-4%2A%28x%2B12%29-22+%29.
Moved these terms to the left highlight_green%28+4%2A%28x%2B12%29+%29,highlight_green%28+22+%29
It becomes -9%2Ax%2B15%2Bhighlight_green%28+4%2A%28x%2B12%29+%29%2Bhighlight_green%28+22+%29=0.
Look at -9%2Ax%2Bhighlight_red%28+15+%29%2B4%2A%28x%2B12%29%2Bhighlight_red%28+22+%29=0.
Added fractions or integers together
It becomes -9%2Ax%2Bhighlight_green%28+37+%29%2B4%2A%28x%2B12%29=0.
Look at -9%2Ax%2Bhighlight_red%28+37+%29%2B4%2A%28x%2B12%29=0.
Moved 37 to the right of expression
It becomes -9%2Ax%2B4%2A%28x%2B12%29%2Bhighlight_green%28+37+%29=0.
Look at -9%2Ax%2Bhighlight_red%28+4%2A%28x%2B12%29+%29%2B37=0.
Expanded term 4 by using associative property on %28x%2B12%29
It becomes -9%2Ax%2Bhighlight_green%28+4%2Ax+%29%2Bhighlight_green%28+4%2A12+%29%2B37=0.
Look at -9%2Ax%2B4%2Ax%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+12+%29%2B37=0.
Multiplied numerator integers
It becomes -9%2Ax%2B4%2Ax%2Bhighlight_green%28+48+%29%2B37=0.
Look at -9%2Ax%2B4%2Ax%2Bhighlight_red%28+48+%29%2Bhighlight_red%28+37+%29=0.
Added fractions or integers together
It becomes -9%2Ax%2B4%2Ax%2Bhighlight_green%28+85+%29=0.
Look at -highlight_red%28+9%2Ax+%29%2Bhighlight_red%28+4%2Ax+%29%2B85=0.
Eliminated similar terms highlight_red%28+-9%2Ax+%29,highlight_red%28+4%2Ax+%29 replacing them with highlight_green%28+%28-9%2B4%29%2Ax+%29
It becomes highlight_green%28+%28-9%2B4%29%2Ax+%29%2B85=0.
Look at %28-highlight_red%28+9+%29%2Bhighlight_red%28+4+%29%29%2Ax%2B85=0.
Added fractions or integers together
It becomes %28highlight_green%28+-5+%29%29%2Ax%2B85=0.
Look at %28highlight_red%28+-5+%29%29%2Ax%2B85=0.
Removed extra sign in front of -5
It becomes %28-highlight_green%28+5+%29%29%2Ax%2B85=0.
Look at highlight_red%28+%28-highlight_red%28+5+%29%29%2Ax+%29%2B85=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes -highlight_green%28+5+%29%2Ax%2B85=0.
Look at highlight_red%28+-5%2Ax%2B85+%29=0.
Solved linear equation highlight_red%28+-5%2Ax%2B85=0+%29 equivalent to -5*x+85 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=17.

Universal Simplifier and Solver


Done!


The mistake you made was when you distributed -4%28x%2B12%29 you forgot to distribute the negative sign along with the 4. -4x-48 is the correct answer.
Hope this helps!