Question

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

Answer 1

`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`