Solve and graph the absolute value inequality: |4x + 1| ≤ 5.

Solution:

Given inequality is

|4x + 1| ≤ 5

-5 ≤ 4x + 1 ≤ 5

Add -1 on all sides

-5 - 1 ≤ 4x + 1 - 1 ≤ 5 - 1

-6 ≤ 4x ≤ 4

Divide by 4

-6/4 ≤ x ≤ 1

-3/2 ≤ x ≤ 1

Therefore, the solution for the given inequality is the region between x = -3/2 and x = 1

Solve and graph the absolute value inequality: |4x + 1| ≤ 5.

Summary:

By Solving the absolute value inequality: |4x + 1| ≤ 5, graph is as shown.