How do you solve #1/3x+2=5/6#?

2 Answers
Feb 26, 2017

Answer:

See the entire solution process below:

Explanation:

First, subtract #color(red)(2)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#1/3x + 2 = 5/6#

#1/3x + 2- color(red)(2) = 5/6 - color(red)(2)#

#1/3x + 0 = 5/6 - (6/6 xx color(red)(2))#

#1/3x = 5/6 - 12/6#

#1/3x = -7/6#

Now, multiply each side of the equation by #color(red)(3)# to solve for #x# while keeping the equation balanced:

#color(red)(3) xx 1/3x = color(red)(3) xx -7/6#

#cancel(color(red)(3)) xx 1/color(red)(cancel(color(black)(3)))x = cancel(color(red)(3)) xx -7/(color(red)(cancel(color(black)(6)))2)#

#x = -7/2#

Feb 26, 2017

Answer:

#x=-7/2# or #3 1/2#

Explanation:

#1/3 x+2=5/6#

#:.x/3+2/1=5/6#

#:.(2x+12=5)/6#

#:.(2x)/6+12/6=5/6#

multiply L.H.S. and R.H.S by 6

#:.2x+12=5#

#:.2x=5-12#

#:.2x=-7#

#x=-7/2#

substitute #x=-7/2#

#:.1/3(-7/2)+2=5/6#

#:.-7/6+12/6=5/6#

#:.5/6=5/6#