Algebra-2

To identify the absolute value inequality that generates the given graph, we analyze the inequality options provided.

From the graph, it is evident that the solution set is -8 ≤ x ≤ 6.

 

Analyze the Inequalities

A. 4|x + 1| > 28

Dividing both sides by 4:

|x + 1| > 7

This leads to two inequalities:

x + 1 > 7 or x + 1 < -7

 

From x + 1 > 7:

x > 6

 

From x + 1 < -7:

x < -8

The solution set is x < -8 or x > 6, which does not match the graph.

 

B. 4|x + 1| ≥ 28

Dividing both sides by 4:

|x + 1| ≥ 7

This leads to two inequalities:

x + 1 ≥ 7 or x + 1 ≤ -7

 

From x + 1 ≥ 7:

x ≥ 6

 

From x + 1 ≤ -7:

x ≤ -8

The solution set is x ≤ -8 or x ≥ 6, which does not match the graph.