How do you solve abs(-2x -5) + 2 > 9?

1 Answer
Mar 16, 2018

The solution set S = {x in RR | (x< -6) or (x>2)}

Explanation:

First let's clean up:

abs(-2x-5) > 7

We have to distinguish two cases:

(1) (-2x-5) > 7 which is obvious ;-)

and

(2) (-2x-5) < -7 which is true, because the absolute of a nuber <-7 is >7.

Lets solve case (1) with some cleanup:

-2x-5 > 7

-2x>12

x<-6

and case (2) results as follows:

-2x-5 < -7

-2x < -2

x > 2

The solution set S = {x in RR | (x< -6) or (x>2)}