Answer:
[tex]-1<x<\frac{-1}{2}[/tex].
Step-by-step explanation:
We have the inequality
[tex]8\left|x+\frac{3}{4}\right| <2[/tex]
[tex]\left|x+\frac{3}{4}\right| <\frac{2}{8}[/tex]
[tex]\left|x+\frac{3}{4}\right| <\frac{1}{4}[/tex]
The property we need to use is the property of the "less or equal":
|a+b|< c is the same as -c < a+b < c. Then
[tex]-\frac{1}{4}<x+\frac{3}{4} <\frac{1}{4}[/tex]
[tex]-\frac{1}{4}-\frac{3}{4} <x<\frac{1}{4}-\frac{3}{4}[/tex]
[tex]-1<x<\frac{-2}{4}[/tex]
[tex]-1<x<\frac{-1}{2}[/tex].
The graph is showed in the picture below.
