How do you solve for x: 5(x-3)+2(3-x)=12?

2 Answers
Jun 22, 2016

You first work away the parentheses

Explanation:

->(5*x-5*3)+(2*3-2*x)=12
(these brackets only used for clarification)

->5x-15+6-2x=12->3x-9=12

Add 9 to both sides:
->3x-cancel9+cancel9=12+9
->3x=21->x=7

Jun 22, 2016

Just a different approach

x=7

Explanation:

Given:" "5(x-3)+2(3-x)=12

If we can change 2(3-x)" such that "(3-x)" became "(x-3) then we have a common factor.

Note that
-2(x-3) = -2x+6" "->" "+2(3-x)=-2x+6

Write the given equation as:

5(x-3)-2(x-3)=12

Factor out (x-3)

(x-3)(5-2)=12

3(x-3)=12

Divide both sides by 3

x-3=4

Add 3 to both sides

x=7