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 ≥ 4. This means the values of (x) fall outside the interval (1, 4).

 

Analyze the Inequalities

A. |5 - 2x| > 3

This translates to:

5 - 2x > 3 or 5 - 2x < -3

 

From 5 - 2x > 3:

-2x > -2
x < 1

 

From 5 - 2x < -3

−2x < −8 ⟹  x > 4

The solution set is x < 1 or x > 4, which does not match the graph.

 

 

B. |5 - 2x| ≥ 3

This translates to:

5 - 2x ≥ 3 or 5 - 2x ≤ -3

 

From 5 - 2x ≥ 3:

-2x ≥ -2
x ≤ 1

 

From 5 - 2x ≤ -3

−2x ≤ −8 ⟹  x ≥ 4

The solution set is x ≤ 1 or...