Question

2/3 (2x-1)=5/6 (x+1) What is x?

Answer 1

`9/8`

Explanation:

`2/3(2x-1)=5/6`
Distribute `2/3`:
`4/3x-2/3=5/6`
Add `2/3` to both sides:
`4/3x=5/6+2/3`
Divide both sides by 4/3:
`x=3/2\div4/3`
`x = 9/8`

Answer 2

Distribute then solve for x. x=3

Explanation:

1. `2/3(2x-1)=5/6(x+1)`

Multiply each fraction on the outside of the parenthesis by the constants inside the parenthesis.

`4/3x-2/3=5/6x+5/6`

Now add `2/3` to each side and subtract `5/6x` from each side.

Find a common denominator and add `5/6 and 2/3`
`5/6+2/3=5/6+4/6=9/6=3/2`

Again, find a common denominator and subtract `4/3x and 5/6x`
`4/3x-5/6x=8/6x-5/6x=3/6x=1/2x`

Now solve `1/2x=3/2`

Divide both side by `1/2`
`(1/2x)/(1/2)=(3/2)/(1/2)`

Multiple the reciprocal `3/2*2/1=3`

You're left with x=3