What is the value of x in the equation #2/3(1/2x+12)=1/2(1/3x+14)-3#?

1 Answer
Jan 12, 2017

#x=-24#

Explanation:

We start with #2/3(1/2x+12)=1/2(1/3x+14)-3#.

The first thing we do is distribute the #2/3# and #1/2#.

That gives us #2/6x+8=1/6x+7-3#.

If we simplify the equation, we get #2/6x+8=1/6x+4#.

Now we just subtract #1/6x# on both sides and subtract #8#.

#2/6x-1/6x=4-8# or #1/6x=-4#.

Just multiply both sides by #6# and we find #x#.

#cancel(color(blue)(6))*1/cancel(6)x=-4*color(blue)(6)# or #color(red)(x=-24)#.

Just to make sure we're right, let's plug #-24# in for #x# and solve.

#2/3(1/2*color(red)(-24)+12)=1/2(1/3*color(red)(-24)+14)-3#

#2/3(-12+12)=1/2(-8+14)-3#

#0=1/2*6-3#

#0=3-3#

#0=0#

We were right! #x=-24#