Question

WILL FAN & GIVE MEDAL FOR ANSWER. Solve and graph the absolute value inequality: |4x + 1| ≤ 5.

Answer 1

| 4x + 1| <= 5

4x + 1 <= 5 -- subtract 1 from both sides
4x <= 4 -- divide both sides by 4
x <= 1

-(4x + 1) <= 5 -- distribute through the parenthesis
-4x - 1 <= 5 -- add 1 to both sides
-4x <= 6 -- divide both sides by -4, but remember that when dividing/multiplying by a negative number, the inequality sign changes.
x >= - 6/4 which reduces to x >= - 3/2 (or - 1 1/2)

since there is an equal sign in the problem, there will be closed circles
and we have x <= 1 and x >= - 3/2 (or - 1 1/2)

it can be written like this : -3/2 < = x <= 1
graph : D...or the 4th graph

Answer 2

thank you!