Question

Solve the compound inequality and graph the solutions for fractions or integers: -3 ≤ (-2x - 1) / (-3) ≤ 2

Answer 1

The inequality solved is -5 ≤ x ≤ 5/2, the graph is in the image at the end.

How to solve the compound inequality?

Here we just need to isolate the variable, our inequality is:

-3 ≤ (-2x - 1) / (-3) ≤ 2

First multiply both sides by -3, this will change the direction of both symbols, then we will get:

-3*-3 ≥ (-2x - 1) ≥ 2*-3

9 ≥ (-2x - 1) ≥ -6

Now add 1 in both sides :

9 + 1 ≥ -2x ≥ -6 + 1

10 ≥ -2x ≥ - 5

And divide by -2 both sides again, this changes the directono the symbols again:

10/-2 ≤ x ≤ -5/-2

-5 ≤ x ≤ 5/2

The graph of this inequality is in the image below.