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

2 Answers
Nov 8, 2017

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

Nov 9, 2017

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