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

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Answer 1 · 2017-01-12T02:58:01

$x=-24$

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! $x=-24$

What is the value of x in the equation 2/3(1/2x+12)=1/2(1/3x+14)-32/3(1/2x+12)=1/2(1/3x+14)-3?