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 > 3.

 

Analyze the Inequalities

A. |5x - 10| > 5

This translates to:

5x - 10 > 5 or 5x - 10 < -5

 

From 5x - 10 > 5:

5x > 15
x > 3

 

From 5x - 10 < -5:

5x < 5
x < 1

The solution set is x < 1 or x > 3, which matches the graph.

 

B. |5x - 10| ≥ 5

This translates to:

5x - 10 ≥ 5 or 5x - 10 ≤ -5

 

From 5x - 10 ≥ 5:

5x ≥ 15
x ≥ 3

 

From 5x - 10 ≤ -5:

5x ≤ 5
x ≤ 1

The solution set is x ≤ 1 or x ...