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Distributive-associative-commutative-properties/223600: factor by grouping
7a^2-2bc-7ab+2ac
1 solutions
Answer 167180 by drj(1380) About Me  on 2009-10-08 10:31:05 (Show Source):
You can put this solution on YOUR website!
7a%5E2-2bc-7ab%2B2ac

Step 1. Rearrange the order of terms so we can start grouping

7a%5E2-2bc-7ab%2B2ac=7a%5E2-7ab%2B2ac-2ab=+%287a%5E2-7ab%29%2B%282ac-2bc%29

Step 2. Now factor out 7a from the first group and 2c from the second group.

%287a%5E2-7ab%29%2B%282ac-2bc%29=+7a%28a-b%29%2B2c%28a-b%29

Step 3. We see that (a-b) is a common factor in the two groups, so factor it out...

7a%28a-b%29%2B2c%28a-b%29=%28a-b%29%287a%2B2c%29

Step 4. ANSWER: 7a%5E2-2bc-7ab%2B2ac=%28a-b%29%287a%2B2c%29


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Linear-equations/223654: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and as dependent or independent.
5x-4y=-28
4y-5x=28
What is the solution of the system of equations?
A. A point
B. No solution
C. Infinitely many solutions
Is the system consistent or inconsistent?
Are the equations dependent or independent?
1 solutions
Answer 167178 by drj(1380) About Me  on 2009-10-08 10:22:56 (Show Source):
You can put this solution on YOUR website!
Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and as dependent or independent.
5x-4y=-28 Equation 1
4y-5x=28 Equation 2 or writing as -5x+4y=28 multiplying by -1 to both sides leads to an identical Equation 1. That is, Equations 1 and 2 are identical.

What is the solution of the system of equations?
A. A point
B. No solution
C. Infinitely many solutions (ANSWER)

Is the system consistent or inconsistent? consistent

Are the equations dependent or independent? dependent

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J






Geometry_Word_Problems/223655: a rectangle carpet has a perimeter of 236 inches. The length of the carpet is 22 inches more than the width. what are the carpets dimensions...?
1 solutions
Answer 167177 by drj(1380) About Me  on 2009-10-08 10:18:47 (Show Source):
You can put this solution on YOUR website!
A rectangle carpet has a perimeter of 236 inches. The length of the carpet is 22 inches more than the width. what are the carpets dimensions...?

Step 1. Perimeter P means adding up all 4 sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let w+22 be the length.

Step 4. Then, P=w+w+w+22+w+22=4w+44=236

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: w=48.
  • Graphical form: Equation 4w%2B44=236 was fully solved.
  • Text form: 4w+44=236 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4w%2B44=236+%29
    For tutors: simplify_cartoon( 4w+44=236 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Aw%2B44=highlight_red%28+236+%29.
Moved these terms to the left highlight_green%28+-236+%29
It becomes 4%2Aw%2B44-highlight_green%28+236+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+44+%29-highlight_red%28+236+%29=0.
Added fractions or integers together
It becomes 4%2Aw%2Bhighlight_green%28+-192+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+-192+%29=0.
Removed extra sign in front of -192
It becomes 4%2Aw-highlight_green%28+192+%29=0.
Look at highlight_red%28+4%2Aw-192+%29=0.
Solved linear equation highlight_red%28+4%2Aw-192=0+%29 equivalent to 4*w-192 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=48.

Universal Simplifier and Solver


Done!



With w=48 and w%2B22=70. And P=2%2848%2B70%29=236 which is a true statement

Step 5. ANSWER: The width is 48 inches and the length is 70 inches.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Systems-of-equations/223656: Solve the following system of equations.
x+7y=9 (1)
x=3-7y (2)
What is the solution of system? Select the correct choice below and if necessary, fill in the answer box to complete your choice.
A. The solution is_____. (Type an ordered pair.)
B. There is no solution.
1 solutions
Answer 167176 by drj(1380) About Me  on 2009-10-08 10:15:34 (Show Source):
You can put this solution on YOUR website!
Solve the following system of equations.

x+7y=9 (1)
x=3-7y (2) or x+7y=3 (3) after putting 7y on the right side.

What is the solution of system? Select the correct choice below and if necessary, fill in the answer box to complete your choice.
A. The solution is_____. (Type an ordered pair.)
B. There is no solution.

Note subtracting equation (3) from (1) leads to 0=6 which is not a true statement.

Also note that the left side of equations (1) and (3) are identical (which implies they have the same slope. Lines with the same slope do not intersect and therefore have no solution.

So ANSWER is B.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J


Word_Problems_With_Coins/223618: John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution
1 solutions
Answer 167174 by drj(1380) About Me  on 2009-10-08 10:06:44 (Show Source):
You can put this solution on YOUR website!
John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution

Step 1. Let x be the number of quarters.

Step 2. Let 0.25x be the dollar value of quarters.

Step 3. Let y be the number of dimes.

Step 4. Let 0.10y be the dollar value of dimes.

Step 5. Then 0.25x+0.10y=2.05 be the total dollar value.

Step 6. Also, y=x+3 since there are 3 more dimes than quarters

Step 7. Our linear system of equation is given in Steps 4 and 5 shown below:

0.25x%2B0.10y=2.05
-x%2By=3

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 0.1*y to the right, we get:
0.25%2Ax+=+2.05+-+0.1%2Ay, or x+=+2.05%2F0.25+-+0.1%2Ay%2F0.25. Substitute that
into another equation:
-1%2A%282.05%2F0.25+-+0.1%2Ay%2F0.25%29+%2B+1%5Cy+=+3 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



So x=5 and y=8. The difference is 3 and the total dollar value is 0.25*5+0.10*8=2.05 which is a true statement.

Step 8. ANSWER: The number of quarters is 5 and the number of dimes is 8.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit
http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J



Rectangles/223628: the perimeter of a rectangle is 140 m. The length is 4 m more than twice the width. Find the dimensions.
1 solutions
Answer 167172 by drj(1380) About Me  on 2009-10-08 09:54:30 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 140 m. The length is 4 m more than twice the width. Find the dimensions.

Step 1. Perimeter P means adding up all 4 sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 2w+4 be the length since it's 4 more than twice the width

Step 4. Then, P=w+w+2w+4+2w+4=6w+8=140

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: w=22.
  • Graphical form: Equation 6w%2B8=140 was fully solved.
  • Text form: 6w+8=140 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+6w%2B8=140+%29
    For tutors: simplify_cartoon( 6w+8=140 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 6%2Aw%2B8=highlight_red%28+140+%29.
Moved these terms to the left highlight_green%28+-140+%29
It becomes 6%2Aw%2B8-highlight_green%28+140+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+8+%29-highlight_red%28+140+%29=0.
Added fractions or integers together
It becomes 6%2Aw%2Bhighlight_green%28+-132+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+-132+%29=0.
Removed extra sign in front of -132
It becomes 6%2Aw-highlight_green%28+132+%29=0.
Look at highlight_red%28+6%2Aw-132+%29=0.
Solved linear equation highlight_red%28+6%2Aw-132=0+%29 equivalent to 6*w-132 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=22.

Universal Simplifier and Solver


Done!



With w=22 and 2w%2B4=48. And P=2%2822%2B48%29=140 which is a true statement

Step 5. ANSWER: The width is 22 meters and the length is 48 meters.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Rectangles/223646: The perimeter of a rectangle is 900 yards. What are the dimensions of the rectangle if the length is 30 yards more than the width?
1 solutions
Answer 167170 by drj(1380) About Me  on 2009-10-08 09:50:41 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 900 yards. What are the dimensions of the rectangle if the length is 30 yards more than the width?

Step 1. Perimeter P means adding up all 4 sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let w+30 be the length.

Step 4. Then, P=w+w+w+30+w+30=4w+60=900

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: w=210.
  • Graphical form: Equation 4w%2B60=900 was fully solved.
  • Text form: 4w+60=900 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4w%2B60=900+%29
    For tutors: simplify_cartoon( 4w+60=900 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Aw%2B60=highlight_red%28+900+%29.
Moved these terms to the left highlight_green%28+-900+%29
It becomes 4%2Aw%2B60-highlight_green%28+900+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+60+%29-highlight_red%28+900+%29=0.
Added fractions or integers together
It becomes 4%2Aw%2Bhighlight_green%28+-840+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+-840+%29=0.
Removed extra sign in front of -840
It becomes 4%2Aw-highlight_green%28+840+%29=0.
Look at highlight_red%28+4%2Aw-840+%29=0.
Solved linear equation highlight_red%28+4%2Aw-840=0+%29 equivalent to 4*w-840 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=210.

Universal Simplifier and Solver


Done!



With w=210 and w%2B30=240. And P=2%28210%2B240%29=900 which is a true statement

Step 5. ANSWER: The width is 210 yards and the length is 240 yards.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Numbers_Word_Problems/223553: the difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. find both numbers
1 solutions
Answer 167128 by drj(1380) About Me  on 2009-10-08 00:57:39 (Show Source):
You can put this solution on YOUR website!
The difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find both numbers

Step 1. Let x be one smaller number

Step 2. Let y be the larger number.

Step 3. Then -x+y=12 since the difference of two numbers is 12.

Step 4. 2y%2F5=6%2Bx%2F3 since two fifths of the greater number is six more than one third of the lesser number

Multiply by 15 to get rid of the denominators.

15%2A2y%2F5=15%2A6%2B15x%2F3

6y=90%2B5x

Subtract 5x from both sides of the equation

-5x%2B6y=90

Step 5. So here's our system of linear equations From Steps 3 and 4:

-x%2By=12
-5x%2B6y=90

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++-1%5Cx+%2B+1%5Cy+=+12%2C%0D%0A++++-5%5Cx+%2B+6%5Cy+=+90+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
-1%2Ax+=+12+-+1%2Ay, or x+=+12%2F-1+-+1%2Ay%2F-1. Substitute that
into another equation:
-5%2A%2812%2F-1+-+1%2Ay%2F-1%29+%2B+6%5Cy+=+90 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



Step 6. The numbers are 18 and 30.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J



Geometry_Word_Problems/223573: the perimeter of a rectangular field is 1,200 feet and the field is 50 feet longer than it is wide. what is the length, i feet, of the field?
1 solutions
Answer 167126 by drj(1380) About Me  on 2009-10-08 00:50:50 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangular field is 1,200 feet and the field is 50 feet longer than it is wide. what is the length, in feet, of the field?

Step 1. Perimeter P means adding up all 4 sides of the rectangle.

Step 2. Let w be the width.

Step 3. Let w+50 be the length.

Step 4. Then, P=1200=w+w+w+50+w+50.

Step 5. Solving leads to the following steps...

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: w=275.
  • Graphical form: Equation 1200=w%2Bw%2Bw%2B50%2Bw%2B50 was fully solved.
  • Text form: 1200=w+w+w+50+w+50 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+1200=w%2Bw%2Bw%2B50%2Bw%2B50+%29
    For tutors: simplify_cartoon( 1200=w+w+w+50+w+50 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 1200=w%2Bw%2Bw%2Bhighlight_red%28+50+%29%2Bw%2Bhighlight_red%28+50+%29.
Added fractions or integers together
It becomes 1200=w%2Bw%2Bw%2Bhighlight_green%28+100+%29%2Bw.
Look at 1200=w%2Bw%2Bw%2Bhighlight_red%28+100+%29%2Bw.
Moved 100 to the right of expression
It becomes 1200=w%2Bw%2Bw%2Bw%2Bhighlight_green%28+100+%29.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+w+%29 replacing them with highlight_green%28+%281%2B1%2B1%2B1%29%2Aw+%29
It becomes 1200=highlight_green%28+%281%2B1%2B1%2B1%29%2Aw+%29%2B100.
Look at .
Added fractions or integers together
It becomes 1200=%28highlight_green%28+4+%29%29%2Aw%2B100.
Look at 1200=highlight_red%28+%28highlight_red%28+4+%29%29%2Aw+%29%2B100.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes 1200=highlight_green%28+4+%29%2Aw%2B100.
Look at 1200=highlight_red%28+4%2Aw%2B100+%29.
Moved these terms to the left highlight_green%28+-4%2Aw+%29,highlight_green%28+-100+%29
It becomes 1200-highlight_green%28+4%2Aw+%29-highlight_green%28+100+%29=0.
Look at highlight_red%28+1200+%29-4%2Aw-highlight_red%28+100+%29=0.
Added fractions or integers together
It becomes highlight_green%28+1100+%29-4%2Aw=0.
Look at highlight_red%28+1100+%29-4%2Aw=0.
Moved 1100 to the right of expression
It becomes -4%2Aw%2Bhighlight_green%28+1100+%29=0.
Look at highlight_red%28+-4%2Aw%2B1100+%29=0.
Solved linear equation highlight_red%28+-4%2Aw%2B1100=0+%29 equivalent to -4*w+1100 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=275.

Universal Simplifier and Solver


Done!



w=275 then w%2B50=325 and P=2%28275%2B325%29=1200 which is a true statement.

Step 6. ANSWER: The length of the field is 325 yards.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J


Numbers_Word_Problems/223562: Hi, I don't know how to do consecutive odd/even integers.
Such as this problem:

Find three consecutive integers whose sum is 36.

I know it's x+(x+2)+(x+3). Am I right? After all, they are 'consecutive', they are not odd or even.

Then the other one is:

Find two consecutive even integers whose sum is 126.


I did the first one, x+x+2=126
Then I subtracted two from both sides, and got x+x=124. Then I added like terms and got 2x=124. And then I simply divided by 2. And got 62.
I did the last question from another guy who answered another guy. But he didn't explain HOW to get the other one. I know the other answer is 64...but I do not know how to get it!
Please explain it clearly as I have an Algebra Test tomorrow, and I want to ace it.

Thanks. :)

1 solutions
Answer 167124 by drj(1380) About Me  on 2009-10-08 00:42:32 (Show Source):
You can put this solution on YOUR website!
Find three consecutive integers whose sum is 36.

Step 1. Let n be the first integer.

Step 2. Let n+1 and n+2 be the next two consecutive integers.

Step 3. Then n+n+1+n+2=36 since the sum is 36.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: n=11.
  • Graphical form: Equation n%2Bn%2B1%2Bn%2B2=36 was fully solved.
  • Text form: n+n+1+n+2=36 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B1%2Bn%2B2=36+%29
    For tutors: simplify_cartoon( n+n+1+n+2=36 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2Bn%2Bhighlight_red%28+1+%29%2Bn%2Bhighlight_red%28+2+%29=36.
Added fractions or integers together
It becomes n%2Bn%2Bhighlight_green%28+3+%29%2Bn=36.
Look at n%2Bn%2Bhighlight_red%28+3+%29%2Bn=36.
Moved 3 to the right of expression
It becomes n%2Bn%2Bn%2Bhighlight_green%28+3+%29=36.
Look at highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B3=36.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%2B1%29%2An+%29
It becomes highlight_green%28+%281%2B1%2B1%29%2An+%29%2B3=36.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B3=36.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2An%2B3=36.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2An+%29%2B3=36.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2An%2B3=36.
Look at 3%2An%2B3=highlight_red%28+36+%29.
Moved these terms to the left highlight_green%28+-36+%29
It becomes 3%2An%2B3-highlight_green%28+36+%29=0.
Look at 3%2An%2Bhighlight_red%28+3+%29-highlight_red%28+36+%29=0.
Added fractions or integers together
It becomes 3%2An%2Bhighlight_green%28+-33+%29=0.
Look at 3%2An%2Bhighlight_red%28+-33+%29=0.
Removed extra sign in front of -33
It becomes 3%2An-highlight_green%28+33+%29=0.
Look at highlight_red%28+3%2An-33+%29=0.
Solved linear equation highlight_red%28+3%2An-33=0+%29 equivalent to 3*n-33 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=11.

Universal Simplifier and Solver


Done!



So n=11, n%2B1=12 and n%2B2=13 Note integers add up to 36

Step 4. ANSWER: The integers are 11, 12, and 13.


Find two consecutive even integers whose sum is 126.

Step 1. Let n be the first even integer

Step 2. Let n+2 be the next consecutive even integers

Step 3. Then, n+n+2=126 since the sum is 126.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: n=62.
  • Graphical form: Equation n%2Bn%2B2=126 was fully solved.
  • Text form: n+n+2=126 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B2=126+%29
    For tutors: simplify_cartoon( n+n+2=126 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B2=126.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%29%2An+%29
It becomes highlight_green%28+%281%2B1%29%2An+%29%2B2=126.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B2=126.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2An%2B2=126.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2An+%29%2B2=126.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2An%2B2=126.
Look at 2%2An%2B2=highlight_red%28+126+%29.
Moved these terms to the left highlight_green%28+-126+%29
It becomes 2%2An%2B2-highlight_green%28+126+%29=0.
Look at 2%2An%2Bhighlight_red%28+2+%29-highlight_red%28+126+%29=0.
Added fractions or integers together
It becomes 2%2An%2Bhighlight_green%28+-124+%29=0.
Look at 2%2An%2Bhighlight_red%28+-124+%29=0.
Removed extra sign in front of -124
It becomes 2%2An-highlight_green%28+124+%29=0.
Look at highlight_red%28+2%2An-124+%29=0.
Solved linear equation highlight_red%28+2%2An-124=0+%29 equivalent to 2*n-124 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=62.

Universal Simplifier and Solver


Done!



n=62 and n%2B2=64

Step 4. ANSWER: The consecutive even integers are 62 and 64

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Signed-numbers/223558: For order of operations, what is the correct way to solve this problem? The answer key says 9, but I get 33. What is the correct way to do this problem and why?
36 ÷ 4(5-2)+ 6
1 solutions
Answer 167122 by drj(1380) About Me  on 2009-10-08 00:34:58 (Show Source):
You can put this solution on YOUR website!
For order of operations, what is the correct way to solve this problem? The answer key says 9, but I get 33. What is the correct way to do this problem and why?

36 ÷ 4(5-2)+ 6

Step 1. Do the operation in the parenthesis

36 ÷ 4(3)+ 6

Step 2. Perform 36/4=9

Step 3. 9*3=27

Step 4. 27+6=33 I get the same answer as you!

I think how they got nine is as follows

36/12+6=9 But this is not correct as written. It should be written with an additional set of parenthesis given as follows:

36 ÷ (4(5-2))+ 6

I hope the above steps were helpful.

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Respectfully,
Dr J

Surface-area/223544: How do you find the radius and diameter of a circle with an area of 35 in^2
1 solutions
Answer 167121 by drj(1380) About Me  on 2009-10-08 00:27:27 (Show Source):
You can put this solution on YOUR website!
How do you find the radius and diameter of a circle with an area of 35 in^2

Step 1. The Area A of a circles is given as A=pi%2Ar%5E2=pi%2A%28d%2F2%29%5E2=pi%2Ad%5E2%2F4 where r is the radius and d is the diameter. Also diameter d=2r

Step 2. Then A=pi%2Ar%5E2=35

Step 3. Solving the equation in Step 2 leads to the following steps

Divide by pi to both sides of the equation

r%5E2=35%2Fpi

Take the square root to both sides of the equation

r=sqrt%2835%2Fpi%29 and d=2sqrt%2835%2Fpi%29

Step 4. ANSWER: Radius is sqrt%2835%2Fpi%29 and diameter is 2%2Asqrt%2835%2Fpi%29.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J



Percentage-and-ratio-word-problems/223560: a bus is carrying 180 passengers which is 9/10 its capacity. What is its capacity?
1 solutions
Answer 167120 by drj(1380) About Me  on 2009-10-08 00:18:04 (Show Source):
You can put this solution on YOUR website!
A bus is carrying 180 passengers which is 9/10 its capacity. What is its capacity?

The capacity is 180=x%2A9%2F10 or x=10%2A180%2F9=200

ANSWER: The capacity is 200.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Respectfully,
Dr J

Equations/223557: Please solve 6(5g+2)=30g
1 solutions
Answer 167119 by drj(1380) About Me  on 2009-10-08 00:15:45 (Show Source):
You can put this solution on YOUR website!
Please solve 6(5g+2)=30g

Step 1. Multiply out the terms to get rid of the parenthesis.

6%2A5g%2B6%2A2=30g

30g%2B12=30g

Step 2. Subtract 30g from both sides of the equation

30g%2B12-30g=30g-30g

12=0 This is not a true statement.

Step 3. There is no solution to this equation.

I hope the above steps were helpful.

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Respectfully,
Dr J

Linear-systems/223162: x + y + z =8
x – y – z = -4
-x + y – z = -8

1 solutions
Answer 166982 by drj(1380) About Me  on 2009-10-07 18:00:33 (Show Source):
You can put this solution on YOUR website!
x + y + z =8 Equation A
x – y – z = -4 Equation B
-x + y – z = -8 Equation C

Step 1. Add equations A and B where the y and z terms cancel out or eliminated to give:

2x=4 or x=2
Step 2. Add equations B and C where the x and y terms cancel out or eliminated to give:

-2z=-12 or z=6

Step 3. Add equations A and C where the x and z terms cancel out or eliminated to give:

2y=0 or y=0

Step 4. ANSWER: x=2, y=0, and z=6.

Check with original equations which all leads to true statements

x + y + z = 2+0+6 = 8 Equation A
x – y – z = 2-0-6=-4 Equation B
-x + y – z = -2+0-6=-8 Equation C

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J



Exponents/223259: Find each root
cubed root of 8x^6y^3
1 solutions
Answer 166980 by drj(1380) About Me  on 2009-10-07 17:52:30 (Show Source):
You can put this solution on YOUR website!
Find each root

cubed root of 8 x^6 y^3

cube root of 8x%5E6y%5E3=2%5E3%2A%28x%5E2%29%5E3%2Ay%5E3 is 2x%5E2y

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Linear_Equations_And_Systems_Word_Problems/223257: the second number is 3 less than twice the first number. Their sum is 57. Find the second number.
1 solutions
Answer 166978 by drj(1380) About Me  on 2009-10-07 17:49:29 (Show Source):
You can put this solution on YOUR website!
The second number is 3 less than twice the first number. Their sum is 57. Find the second number.

Step 1. Let n be the first number.

Step 2. Let 2n-3 be the second number

Step 3. Then n+2n-3=57 since the sum of the two numbers is 57.

Step 4. Solving the equation in Step 3

3n-3=57

Add 3 to both sides of the equation

3n-3%2B3=57%2B3

3n=60

Divide 3 to both sides of the equation

3n%2F3=60%2F3

n=20 and 2n-3=40-3=37. Note the sum is 57.

Step 5. ANSWER: The second number is 37.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Respectfully,
Dr J



Geometry_Word_Problems/223253: If a wheel travels 1 mile in 1 minute, at a rate of 600 revolutions per minute, what is the diameter of the wheel, in feet?
1 solutions
Answer 166977 by drj(1380) About Me  on 2009-10-07 17:44:52 (Show Source):
You can put this solution on YOUR website!
If a wheel travels 1 mile in 1 minute, at a rate of 600 revolutions per minute, what is the diameter of the wheel, in feet?

Step 1. Let d be the diameter of the wheel.

Step 2. Let pi%2Ad be the circumference of the wheel for one revolution

Step 3. Note 1 mile = 5280 feet

Step 4. Then 1 mile = 5280 ft= 600*pi*d since 600 revolutions occur in one minute.

Step 5. Solving for d=5280%2F%28600%2Api%29=2.80 feet

Step 6. ANSWER: The diameter of the wheel is 2.80 feet.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Respectfully,
Dr J

Square-cubic-other-roots/223215: please help me solve simplify: +sqrt+%282ab%5E2%29+%2A+sqrt+%2814ab%5E2%29+
1 solutions
Answer 166976 by drj(1380) About Me  on 2009-10-07 17:37:00 (Show Source):
You can put this solution on YOUR website!
please help me solve simplify: +sqrt+%282ab%5E2%29+%2A+sqrt+%2814ab%5E2%29+



I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J

Equations/223250: Having trouble with this problem. 2a+3a-13=a+3
1 solutions
Answer 166975 by drj(1380) About Me  on 2009-10-07 17:30:58 (Show Source):
You can put this solution on YOUR website!
Having trouble with this problem. 2a+3a-13=a+3

Step 1. Combine like terms and numbers

2a%2B3a-13=a%2B3

%282%2B3%29a-13=a%2B3

5a-13=a%2B3

Step 2. Add 13 to both sides of the equation to get number on the right side.

5a-13%2B13=a%2B3%2B13

5a=a%2B16

Step 3. Subtract a to both sides of the equation to get a-terms on the left side.

5a-a=a%2B16-a

4a=16

Step 4. Divide 4 to both sides of the equation

4a%2F4=16%2F4

a=4

Check...2a%2B3a-13=a%2B3...2%2A4%2B3%2A4-13=4%2B3...8%2B12-13=7...7=7 which is a true statement.

Step 5. ANSWER: a=4

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J


Systems-of-equations/223154: how do you solve this equation by graphing
x-y=3
x+y=5
1 solutions
Answer 166970 by drj(1380) About Me  on 2009-10-07 17:22:08 (Show Source):
You can put this solution on YOUR website!
How do you solve this equation by graphing

x-y=3
x+y=5

Step 1. Plot the above equation using the slope intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).

Step 2. Put x-y=3 in slope intercept form or y=x-3 where we added y-3 to both sides of the equation. Here the slope m=1 and b=-3.

Step 3. Put x+y=5 in slope intercept form where y=-x+5 where we added -x to both sides of the equation. Here the slope is m=-1 and b=5.

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C+x-3%2C+-x%2B5%29

Step 4. ANSWER: Based on the above graph, the two lines intersect at point (4,1) or x=4 and y=1.

We can check by substituting in the original equations:

x-y=3 or 4-1=3 which is a true statement

x%2By=5 or 4%2B1=5 which is also a true statement.

So the point (4,1) is a solution to the system of equations.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Respectfully,
Dr J


Polynomials-and-rational-expressions/223191: If the sides of a square are lengthened by 8 cm, the area become 256cm^2. Find the length of the original square.
The length of the original square is ? cm.

1 solutions
Answer 166965 by drj(1380) About Me  on 2009-10-07 17:10:22 (Show Source):
You can put this solution on YOUR website!
If the sides of a square are lengthened by 8 cm, the area become 256cm^2. Find the length of the original square.

The length of the original square is ? cm.

Step 1. Let x be the length of the original side of the square.

Step 2. Let x+8 be the length having an area of 256 square centimeters.

Step 3. Area A=(x+8)^2=256 since the area of the square is the square of its side x+8.

Step 4. Solving equation in Step 3 yields the following steps:

%28x%2B8%29%5E2=x%5E2%2B16x%2B64=256

Subtract 256 from both sides of the equation

x%5E2%2B16x%2B64-256=256-256

x%5E2%2B16x-192=0

Step 5. To solve, use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=16, and c=-192.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B16x%2B-192+=+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=%2816%29%5E2-4%2A1%2A-192=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+1024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+1024+%29%29%2F2%5C1+=+8
x%5B2%5D+=+%28-%2816%29-sqrt%28+1024+%29%29%2F2%5C1+=+-24

Quadratic expression 1x%5E2%2B16x%2B-192 can be factored:
1x%5E2%2B16x%2B-192+=+1%28x-8%29%2A%28x--24%29
Again, the answer is: 8, -24. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B16%2Ax%2B-192+%29



Choosing the positive solution x=8. Note %288%2B8%29%5E2=256

Step 6. ANSWER: The length of the side of the original square is 8 cm.


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J





Linear-systems/223232: 9x-5(3x-12)=30
1 solutions
Answer 166958 by drj(1380) About Me  on 2009-10-07 17:01:37 (Show Source):
You can put this solution on YOUR website!
9x-5(3x-12)=30

Step 1. Multiply out the terms to get rid of the parenthesis and be careful or aware of the minus sign:

9x%2B%28-5%29%2A%283x%29%2B+%28-5%29%2A%28-12%29=30

9x-15x-60=30

Step 2. Combine the x-terms and add 60 to both sides of the equation


%289-15%29x-60%2B60=30-60

-6x=-30

Divide by -6 to both sides of the equation


-6x%2F-6=-30%2F-6

x=5

Check...9x-5%283x-12%29=30...9%2A5-5%283%2A5-12%29=30....30=30...a true statement.

Step 3. ANSWER: x=5

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Graphs/223231: I need a real-world example when the solution of a system of linear equations must be in the first quadrant. What do I need to know?
1 solutions
Answer 166955 by drj(1380) About Me  on 2009-10-07 16:55:33 (Show Source):
You can put this solution on YOUR website!
I need a real-world example when the solution of a system of linear equations must be in the first quadrant. What do I need to know?

Here's an example:

Donnie has $5.10 in nickels, dimes, and quarters. He has an equal number of dimes and nickels, with the value of the quarters being $2.40 more than the total value of the dimes and nickels. How many dimes does he have?

Step 1. Let x be the number of nickels

Step 2. Let x be the number of dimes since they are equal in number with the nickels.

Step 3. Let %280.05%2B0.10%29x=0.15x be the dollar values of nickels and dimes.

Step 4. Let 0.25y be the dollar values of quarters.

Step 5. 2.40%2B0.15x=0.25y since the value of the quarters being $2.40 more than the total value of the dimes and nickels. Or rewriting it as

-0.15x%2B0.25y=2.40

Step 6. Also, 0.15x%2B0.25y=5.10 as given by the problem since $5.10 in nickels, dimes, and quarters.

Step 7. Now, we have a linear system of equations in Steps 5 and 6

-0.15x%2B0.25y=2.40 Equation A
0.15x%2B0.25y=5.10 Equation B

Adding Equations A and B

-0.15x%2B0.15x%2B0.25y%2B0.25y=2.40%2B5.10

0.50y=7.50

y=15 quarters

Then solving x from Equation B is 5.10-3.75=0.15x or x=9.

Check Equation A if true -0.15x%2B0.25y=2.40 or -1.35%2B3.75=2.40...which is a true statement.

Step 8. ANSWER: The number of nickels and dimes is 9 each and the number of quarters is 15.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J












Pythagorean-theorem/223128: Find the area of a triangle with a base of 8 yd and a height of 19.1 yd.
1 solutions
Answer 166899 by drj(1380) About Me  on 2009-10-07 14:33:11 (Show Source):
You can put this solution on YOUR website!
Find the area of a triangle with a base of 8 yd and a height of 19.1 yd.

The area A of a triangle is given as

A=bh%2F2

where b is the base and h is the height

A=8%2A19.1%2F2

ANSWER: Area is 76.4 square yards

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for
Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV

expressions/223027: Solve.
8x-(6x+4)=12
The solution of x = ___
1 solutions
Answer 166866 by drj(1380) About Me  on 2009-10-07 11:46:03 (Show Source):
You can put this solution on YOUR website!
Solve.

8x-%286x%2B4%29=12

The solution of x = ___

Step 1. Get rid of the parenthesis by distributing the negative (=-1) and combine line terms

8x-6x-4=12

2x-4=12

Step 2. Add 4 to both sides of the equation

2x-4%2B4=12%2B4


2x=16

Step 3. Divide 8 to both sides of the equation

2x%2F2=16%2F2

x=8

Step 4. ANSWER. The solution is x=8.


I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for
Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV







Linear-systems/223025: The problem isn't explaining it enough for me to understand here's the question
Solve the following system of equations by any method you wish
X + y = 6
Y = 2x – 3

1 solutions
Answer 166864 by drj(1380) About Me  on 2009-10-07 11:42:27 (Show Source):
You can put this solution on YOUR website!
The problem isn't explaining it enough for me to understand here's the question
Solve the following system of equations by any method you wish

x + y = 6
y = 2x – 3 or -2x+y=-3

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+6%2C%0D%0A++++-2%5Cx+%2B+1%5Cy+=+-3+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
1%2Ax+=+6+-+1%2Ay, or x+=+6%2F1+-+1%2Ay%2F1. Substitute that
into another equation:
-2%2A%286%2F1+-+1%2Ay%2F1%29+%2B+1%5Cy+=+-3 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for
Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Respectfully,
Dr J

http://www.FreedomUniversity.TV

Travel_Word_Problems/222988: The second angle of a triangle is 4 times as large as the first. The third angle is 120 degrees more than the sum of the two angles. Find the measure of the second angle.
1 solutions
Answer 166863 by drj(1380) About Me  on 2009-10-07 11:40:54 (Show Source):
You can put this solution on YOUR website!
The second angle of a triangle is 4 times as large as the first. The third angle is 120 degrees more than the sum of the two angles. Find the measure of the second angle.

Step 1. The three angles of a triangle add up to 180 degrees.

Step 2. Let x be the first angle.

Step 3. Let 4x be the second angle since it is 4 times as large as the first.

Step 4. Let x+4x=5x be the sum of the first two angles.

Step 5. Let 5x+120 be the third angle since it is 120 degrees more than the sum of the two angles.

Step 6. Then, x+4x+5x+120=180 degrees.

Step 7. Solving the equation in Step 6 yields the following steps

10x%2B120=180

Subtract 120 from both sides of the equation

10x%2B120-120=180-120

10x=60

Divide 10 to both sides of the equation

10x%2F10=60%2F10

x=6. Then 4x=24 and 5x%2B120=150. Note these three angles add up to 180 degrees.

Step 8. ANSWER: The second angle is 24 degrees.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for
Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV





Age_Word_Problems/222991: Kimberly is twice as old as Ryan. In 4 years, she will be 7 years older than Ryan. How old is Kimberly now?

1 solutions
Answer 166862 by drj(1380) About Me  on 2009-10-07 11:32:56 (Show Source):
You can put this solution on YOUR website!
Kimberly is twice as old as Ryan. In 4 years, she will be 7 years older than Ryan. How old is Kimberly now?

Step 1. Let x be the age of Ryan

Step 2. Let 2x be the age of Kimberly

Step 3. Let x+4 be the age of Ryan in 4 years

Step 4. Let 2x+4 be the age of Kimberly in 4 years.

Step 5. 2x+4=x+4+7 since Kimberly will be 7 years older than Ryan in four years.

Step 6. Solving the equation in Step 5 yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=7.
  • Graphical form: Equation 2x%2B4=x%2B4%2B7 was fully solved.
  • Text form: 2x+4=x+4+7 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2x%2B4=x%2B4%2B7+%29
    For tutors: simplify_cartoon( 2x+4=x+4+7 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2Ax%2B4=x%2Bhighlight_red%28+4+%29%2Bhighlight_red%28+7+%29.
Added fractions or integers together
It becomes 2%2Ax%2B4=x%2Bhighlight_green%28+11+%29.
Look at 2%2Ax%2B4=highlight_red%28+x%2B11+%29.
Moved these terms to the left highlight_green%28+-x+%29,highlight_green%28+-11+%29
It becomes 2%2Ax%2B4-highlight_green%28+x+%29-highlight_green%28+11+%29=0.
Look at 2%2Ax%2Bhighlight_red%28+4+%29-x-highlight_red%28+11+%29=0.
Added fractions or integers together
It becomes 2%2Ax%2Bhighlight_green%28+-7+%29-x=0.
Look at 2%2Ax%2Bhighlight_red%28+-7+%29-x=0.
Moved -7 to the right of expression
It becomes 2%2Ax-x%2Bhighlight_green%28+-7+%29=0.
Look at 2%2Ax-x%2Bhighlight_red%28+-7+%29=0.
Removed extra sign in front of -7
It becomes 2%2Ax-x-highlight_green%28+7+%29=0.
Look at highlight_red%28+2%2Ax+%29-highlight_red%28+x+%29-7=0.
Eliminated similar terms highlight_red%28+2%2Ax+%29,highlight_red%28+-x+%29 replacing them with highlight_green%28+%282-1%29%2Ax+%29
It becomes highlight_green%28+%282-1%29%2Ax+%29-7=0.
Look at highlight_red%28+%282-1%29+%29%2Ax-7=0.
Remove extraneous '1' from product highlight_red%28+%282-1%29+%29
It becomes x-7=0.
Look at highlight_red%28+x-7+%29=0.
Solved linear equation highlight_red%28+x-7=0+%29 equivalent to x-7 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=7.

Universal Simplifier and Solver


Done!



With x=7 then 2x=14


Step 7. ANSWER: Kimberly is 14 years old.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra,
please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

Human-and-algebraic-language/222997: The perimeter of a rectangle is 44 meters. The length is 2 meters more than the three times the width. Find the length.
1 solutions
Answer 166860 by drj(1380) About Me  on 2009-10-07 11:25:48 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 44 meters. The length is 2 meters more than the three times the width. Find the length.

Step 1. The perimeter P means adding up all four sides of a rectangle.

Step 2. Let w be the width

Step 3. Let 3w be three times the width

Step 4. Let 3w+2 be the length since it is 2 meters more than three times the width

Step 5. Then P=w+w+3w+2+3w+2=8w+4=44 since the perimeter P is 44 meters.

Step 6. Solving the equation in Step 4 leads to the following steps

8w%2B4=44

Subtract four from both sides

8w%2B4-4=44-4

8w=40

Divide by 8 to both sides of the equation

8w%2F8=40%2F8

w=5 and 3w+2=15+2=17 and P=2(5+17)=44 which is a true statement.

Step 7. The length is 17 meters.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J





Problems-with-consecutive-odd-even-integers/223001: Find three consecutive even integers whose sum is 36.
1 solutions
Answer 166856 by drj(1380) About Me  on 2009-10-07 11:18:47 (Show Source):
You can put this solution on YOUR website!
Find three consecutive even integers whose sum is 36.

Step 1. Let n be an even integer.

Step 2. Let n+2 and n+4 be the next two consecutive even integers.

Step 3. Then n+n+2+n+4=36 since the sum of these three even integers is 36.

Step 4. Solving yields the following steps

3n%2B6=36

Subtract 6 from both sides of the equation

3n-6=36-6

3n=30

Divide by 3 to both sides of the equation

3n%2F3=30%2F3

n=10 n%2B2=12 nad n%2B4=14. Not these three even integers add up to 36.

Step 5. ANSWER: The three consecutive even integers are 10, 12, and 14.


I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J