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

1 Answer
Mar 11, 2018

#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#