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 x < 1 or x > 9.

 

Analyze the Inequalities

A. -6|x - 5| > -24

Dividing both sides by -6 (and flipping the inequality sign):

|x - 5| < 4

This leads to:

-4 < x - 5 < 4

 

From (-4 < x - 5):

1 < x

 

From (x - 5 < 4):

x < 9

The solution set is 1 < x < 9, which does not match the graph.

 

B. -6|x - 5| ≥ -24

Dividing both sides by -6 (and flipping the inequality sign):

|x - 5| ≤ 4

This leads to:

-4 ≤ x - 5 ≤ 4

 

From (-4 ≤ x - 5):

1 ≤ x

 

From (x - 5 ≤ 4):

x ≤ 9

The solution set is 1 ≤ x ≤ 9, which does not ma...