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

1 Answer
Gazza
Mar 11, 2018

m < -2 or m > -1m<−2orm>−1

Explanation:

|-3 - 2m| -8> -7|−3−2m|−8>−7

Let start by adding 88 on both sides

|-3-2m|-8+8> -7+8|−3−2m|−8+8>−7+8

|-3-2m| > 1|−3−2m|>1

Then solve for the absolute value.

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

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

-2m - 3 > 1−2m−3>1

Add 33 on both sides

-2m - 3 + 3 > 1+3−2m−3+3>1+3

-2m > 4−2m>4

Divide both sides by -2−2

(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

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