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