How do you solve 2/3(3x-5)-1/2(4x+3)=1/4(2x-1)-1/1223(3x−5)−12(4x+3)=14(2x−1)−112?

1 Answer
Haunt
Nov 6, 2015

x=-9x=−9

Explanation:

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

2/3*(3x)=2x23⋅(3x)=2x
2/3*(-5)=-10/323⋅(−5)=−103

(The subtraction here is distributed as a negative)

-1/2*(4x)=-2x−12⋅(4x)=−2x
-1/2*(3)=-3/2−12⋅(3)=−32

1/4*(2x)=1/2x14⋅(2x)=12x
1/4*(-1)=-1/414⋅(−1)=−14

This leaves us with:

2x-10/3-2x-3/2=1/2x-1/4-1/122x−103−2x−32=12x−14−112

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-1/3−296=12x−13

Add 1/313 to both sides

-29/6+1/3=1/2x-1/3+1/3−296+13=12x−13+13

-27/6=1/2x−276=12x

Multiply both sides by 2

-27/6*2=1/2x*2−276⋅2=12x⋅2

-27/3=x−273=x

Simplify

x=-9x=−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)-1/4-1/122(−9)−103−2(−9)−32=12(−9)−14−112

Simplify
-18-10/3+18-3/2=-9/2-1/4-1/12−18−103+18−32=−92−14−112

-29/6=-19/4-1/12−296=−194−112

-29/6=-58/12−296=−5812

-29/6=-29/6−296=−296

Our answer is correct!

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