Question

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

number line with closed dots on -3 and 2 with shading going in the opposite directions.

number line with closed dots on -3 and 2 with shading in between.

number line with open dots on -3 and 2 with shading in between.

number line with closed dots on -2 and 2 with shading in between.

Answer 1

| 2x + 1 | <= 5

-5 <= 2x + 1 <= 5 --- subtract 1
-1 - 5 <= 2x <= 5 - 1
-6 <= 2x <= 4 --- divide by 2
-3 <= x <= 2
so basically this is saying that x is greater or equal to -3, bu less or equal to 2

if there is an equal sign, the it has a closed circle
< less then, means shaded to the left
> greater then, means shaded to the right

solution : closed circle on -3, closed circle on 2, shaded in between