Solve and graph the absolute value inequality: |2x + 1| ≤ 5.

Solution:

Given inequality is |2x + 1| ≤ 5

In case of inequality modulus, we take as -5 ≤ 2x + 1 ≤ 5

Add -1 on both sides

-5-1 ≤ 2x + 1 - 1 ≤ 5 - 1

-6 ≤ 2x ≤ 4

Divide by 2 on both sides

-3 ≤ x ≤ 2

Solve and graph the absolute value inequality: |2x + 1| ≤ 5.

Summary:

The absolute value inequality: |2x + 1| ≤ 5 is -3 ≤ x ≤ 2.