absolute value inequalites

Question

1. Solve: -|0.6x + 0.4| < 8

a. x > 2/3 or x < -2

b. -2 < x < 2/3

c. All real numbers

d. No solution

 

 

2. Solve: -|0.6x + 0.4| > 8

a. x > 2/3 or x < -2

b. -2 < x < 2/3

c. All real numbers

d. No solution

Answer 1

-|0.6x + 0.4| < 8

-8<-(0.6x + 0.4) < 8

 

-8+0.4<-0.6x < 8+0.4

 

-7.6<-0.6x < 8.4 (divide both sides by -0.6)

7.6/0.6>x>-8.4/0.6

 

-8<x<38/3. (=12+2/3)

This the solution of original inequality.