Question

How do you solve `8( 12- 2x ) = 5x + 12`?

Answer 1

`x = 4`

Explanation:

Multiply out the brackets

`8 xx 12 = 96`

`8 xx (-2x) = -16x`

to give

`96 - 16x`

on the left side of the equation. Therefore

`96 - 16x = 5x + 12`

Then rearrange the whole equation to get all the `x`'s on one side of the equation.

Add `16x` to both sides of the equation to eliminate the `-16x` from the left side, and minus `12` from both sides to eliminate the `+12` from the right side. This means all the `x`'s are on the left side.

`96 - 12 = 5x +16x`

`84 = 21x`

Divide both sides of the equation by `21` to get the `x` term on its own.

`84/21 = (21x)/21`

Therefore

`x = 4`

In order to ensure the `x` term is correct, be sure to sub it back into the original equation to make sure it works.

Answer 2

By opening up the bracket

Explanation:

`8(12-2x)=5x+12`

`96-16x=5x+12`

So

`21x=84`

`x=4`

Answer 3

Simplifying for x gives us: 4

Explanation:

To start solving this, we need to distribute the 8 to the left side of the equal sign to simplify it.

So distributing the 8 on the left side, gives us: `96-16x`

So we have `96-16x=5x+12`

We can do a couple of things of subtracting `x` on both sides or numbers on both sides. Let's subtract 5x from both sides which gives us:

`96-21x=12`

Now, let subtract 96 to both sides which gives us:

`-21x=-84`

We can divide both sides by -21 which gives us: 4.