Question

1. Solve |x|>5 A. {-5,5} B. x C. x < -5 or x > 5

2. Solve |x|>5 A. {-5,5} B. x C. x < -5 or x > 5

3. Solve |4x-8| <12

Answer 1

1. The given absolute value inequality is:

`|x| \: > \: 5`

This implies that;

`- x \: > \: 5 \: or \: x \: > \: 5`

We the first inequality by -1 and reverse the sign to get:

`x \: < - \: 5 \: or \: x \: > \: 5`

The correct answer is

C. x < -5 or x > 5

2. The given inequality is:

`|4x - 8| \: < \: 12`

This implies that,

`- (4x - 8) \: < \: 12 \: or \: (4x - 8) \: < \: 12`

Divide through the first inequality by -1 and reverse the sign

`4x - 8\: > \: - 12 \: or \: 4x - 8\: < \: 12`

Group similar terms:

`4x \: > \: - 12 + 8 \: or \: 4x \: < \: 12 + 8`

Simplify:

`4x \: > \: - 4\: or \: 4x \: < \: 20`

Divide both sides by 4

`x \: > \: - 1\: or \: x \: < \: 5`