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 1 < x < 9. This means the values of (x) fall within the interval (1, 9).

 

Analyze the Inequalities

A. 2|x - 5| + 3 > 11 ⟹ 2|x - 5| > 8 ⟹ |x - 5| > 4

This translates to:

x - 5 > 4 or x - 5 < -4

 

From x - 5 > 4:

x > 9

 

From x - 5 < -4:

x < 1

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

 

B. 2|x - 5| + 3 ≥ 11 ⟹ 2|x - 5| ≥ 8 ⟹ |x - 5| ≥ 4

This translates to:

x - 5 ≥ 4 or x - 5 ≤ -4

 

From x - 5 ≥ 4:

x ≥ 9

 

From x - 5 ≤ -4:

x ≤ 1

The solution set is x ≤ 1 or x ≥ 9,...