SOLUTION: If 4 is added to twice a number and this sum is multiplied by 2, the result is the same as if the number is multiplied by 3 and 4 is added to the product. What is the number?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If 4 is added to twice a number and this sum is multiplied by 2, the result is the same as if the number is multiplied by 3 and 4 is added to the product. What is the number?      Log On


   

Question 121291: If 4 is added to twice a number and this sum is multiplied by 2, the result is the same as if the number is multiplied by 3 and 4 is added to the product. What is the number?
Answer by solver91311(24713) About Me  (Show Source):
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The number: x

Twice the number: 2x

4 added to twice a number: 2x%2B4

This sum multiplied by 2: 2%282x%2B4%29 RESULT 1

The number multiplied by 3: 3x

4 added to the product: 3x+%2B+4 RESULT 2

The results are the same means that they are equal, so:

2%282x%2B4%29=3x+%2B+4

Distribute the 2:
4x%2B8=3x%2B4

Add -3x to both sides:
4x-3x%2B8=3x-3x%2B4
x%2B8=4

Add -8 to both sides:
x%2B8-8=4-8
x=-4

Check the answer:
Add 4 to twice the number 2%28-4%29%2B4=-4, then multiply by 2 -8

Three times the number is -12, add 4, -8. The results are the same. Answer checks.