Algebra-1

To determine which absolute value inequality corresponds to the solution set (-∞, -2] ∪ [6, ∞), let's analyze each option.

 

Option A, |2x + 3| > 7

Break down the absolute value inequality:

2x + 3 > 7 or 2x + 3 < -7

Solve for x:

For 2x + 3 > 7:

2x + 3 - 3 > 7 - 3

2x > 4

2x/2 > 4/2

x > 2

For 2x + 3 < -7:

2x + 3 < -7 - 3

2x < -10

2x/2 < -10/2

x < -5

The solution set is (-∞, -5)∪ (2, ∞), which does not match the given solution set.

 

Option B, |2x + 3| ≤ 7

Break down the absolute value inequality:

-7 ≤ 2x + 3 ≤ 7

-7 - 3 ≤ 2x + 3 - 3 ≤ 7 - 3

-10 ≤ 2x ≤ 4

-10/2 ≤ 2x/2 ≤ 4/2...