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 0 < x < 2.

 

Analyze the Inequalities

A. 4 + 6|x - 1| ≤ 10

Subtracting 4 from both sides:

6|x - 1| ≤ 6

Dividing both sides by 6:

|x - 1| ≤ 1

This leads to:

-1 ≤ x - 1 ≤ 1

 

From -1 ≤ x - 1:

0 ≤ x

 

From x - 1 ≤ 1:

x ≤ 2

The solution set is 0 ≤ x ≤ 2, which includes 0 and 2, so it does not match the graph.

 

B. 4 + 6|x - 1| > 10

Subtracting 4 from both sides:

6|x - 1| > 6

Dividing both sides by 6:

|x - 1| > 1

This leads to:

x - 1 > 1 or x - 1 < -1:

 

From x − 1 > 1:

x > 2

 

From x − 1 < −1:

x < 0

The solution set is x < 0 or x > 2, which does not match the gra...