Question

-34-) -2 103 11-4k12-11 KB 3-4 .-31>1 Q: 75 ||L4K U L-1 Name Samantha cebolos Kuta Software - Infinite Algebra 2 Absolute Value Inequalities Date 32/2001 Solve each inequality and graph its solution. 2) | p +4158 S8

Answer 1

3 + 4I 3x + 7 I ≥ -89

4I 3x + 7 I ≥ -89 - 3 (Subtracting 3 on both sides of the inequality)

4I 3x + 7 I ≥ -92 (Adding like terms)

I 3x + 7 I ≥ -92/4 (Dividing by 4 on both sides of the inequality)

I 3x + 7 I ≥ -23

Separating the inequality into two inequalities , we have:

3x + 7 ≥ -23 (Inequality 1) and -(3x + 7) ≥ -23 (Inequality 2)

Inequality 1:

3x + 7 ≥ -23

3x ≥ -23 - 7 (Subtracting 7 on both sides of the inequality)

3x ≥ - 30 (Adding like terms)

x ≥ - 30/3 (Dividing by 4 on both sides of the inequality)

x ≥ -10 (Dividing)

Inequality 2:

-(3x + 7) ≥ -23

-3x - 7 ≥ -23 (Distributing)

-3x ≥ -23 + 7 (Adding 7 on both sides of the inequality)

-3x ≥ -16 (Subtracting)

x ≤ -16/-3 (Dividing by -3 on both sides of the inequality)

x ≤ 16/3 (Using the sign rules)

The graph would be:

We see that all real numbers satisfy the inequality.