Expert: Paul Klarreich - 8/28/2011

Question
Solve:
(-3/4)m ≥ m-1 or (-3/4)m < m+1

Sorry about the parenthesis problem. I just wrote what was written on the worksheet.

Answer
Questioner:Maxine
Country:Illinois, United States
Category:Advanced Math
Private:No
Subject:Alg. 2/Trig - Compound Inequalities

Question:

Solve:
(-3/4)m ≥ m-1 or (-3/4)m < m+1

Sorry about the parenthesis problem. I just wrote what was written on the worksheet.
.....................................

That's better.  OK, now -- start by clearing fractions.

(-3/4)m ≥ m-1 or (-3/4)m < m+1

-3m ≥ 4m - 4 or -3m < 4m + 4    <<<< times 4

4  ≥ 7m   or -4 < 7m   <<<< simplify

7m <= 4  or 7m > -4    <<<< reverse, to make it read better

m <= 4/7  or m > -4/7    <<<< divide

A. m <= 4/7  or  B. m > -4/7    <<<< Labels

A. <<---------------------------------------------X
B.         O--------------------------------------------->
-1 -----------------------------0--------------------------- +1

Since the word was 'OR', it's actually the whole line.
(if it had said 'AND', you would have the segment in between, counting +4/7, but not counting -4/7)