How do you solve 2/3(3x-5)-1/2(4x+3)=1/4(2x-1)-1/12?

1 Answer
Nov 6, 2015

x=-9

Explanation:

The first step in this situation is to distribute all values outside of parenthesis

2/3*(3x)=2x
2/3*(-5)=-10/3

(The subtraction here is distributed as a negative)

-1/2*(4x)=-2x
-1/2*(3)=-3/2

1/4*(2x)=1/2x
1/4*(-1)=-1/4

This leaves us with:

2x-10/3-2x-3/2=1/2x-1/4-1/12

Combine all like terms (like terms have the same variables attached) (There is a lot of fractional addition but I'm assuming you can calculate those yourself c: )

-29/6=1/2x-1/3

Add 1/3 to both sides

-29/6+1/3=1/2x-1/3+1/3

-27/6=1/2x

Multiply both sides by 2

-27/6*2=1/2x*2

-27/3=x

Simplify

x=-9

You can check your answer by substituting this value for x in the equation (you need to distribute to solve anyway so I won't repeat that step)
2(-9)-10/3-2(-9)-3/2=1/2(-9)-1/4-1/12

Simplify
-18-10/3+18-3/2=-9/2-1/4-1/12

-29/6=-19/4-1/12

-29/6=-58/12

-29/6=-29/6

Our answer is correct!