Question

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

Answer 1

`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!