Question

Solve and graph the absolute value inequality: |4x + 1| ≤ 5. a. number line with closed dots on −1.5 and 1 with shading going in the opposite directions.
b. number line with open dots on −1.5 and 1 with shading in between. c. number line with closed dots on −1 and 1 with shading in between. d. number line with closed dots on −1.5 and 1 with shading in between.

Answer 1

4x + 1 <= 5               ;  x = 1

4x +1 >=  -5              ;  x = - 1.5

Now we know that x is between -1.5 and 1, so you should shade between -1.5 and 1. The circle will be closed since the equality is =< and =>

The answer is option D

Hope this helps