Question

How do you solve `|- 3- 2m | - 8> - 7`?

Answer 1

`m < -2 or m > -1`

Explanation:

`|-3 - 2m| -8> -7`

Let start by adding `8` on both sides

`|-3-2m|-8+8> -7+8`

`|-3-2m| > 1`

Then solve for the absolute value.

We know either `-2m - 3 > 1 or -2m - 3 < -1`

So here we have two possibilities. Solve the first one!

`-2m - 3 > 1`

Add `3` on both sides

`-2m - 3 + 3 > 1+3`

`-2m > 4`

Divide both sides by `-2`

`(cancel(-2)m)/cancel(-2)>4/(-2)`

`m < -2`

Note: When you are solving inequalities, whenever you divide both sides by a negative number, you MUST change the sign(symbol).

Now solve the second possibility

`-2m - 3 < -1`

Add `3` on both sides

`-2m - 3 + 3 < -1 + 3`

`-2m < 2`

Divide both sides by `-2`

`(cancel(-2)m)/cancel(-2) < 2/(-2)`

`m > -1`

Thus,

The answers are: `m < -2 or m> -1`