Question

Solve the inequality. graph the solution set.

8|x+3/4|<2

Answer 1

These are the steps to solving. In order.

Answer 2

`-1<x<(-1)/(2)`.

Explanation:

We have the inequality

`8\left|x+(3)/(4)\right| <2`

`\left|x+(3)/(4)\right| <(2)/(8)`

`\left|x+(3)/(4)\right| <(1)/(4)`

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

`-(1)/(4)<x+(3)/(4) <(1)/(4)`

`-(1)/(4)-(3)/(4) <x<(1)/(4)-(3)/(4)`

`-1<x<(-2)/(4)`

`-1<x<(-1)/(2)`.

The graph is showed in the picture below.