If 13≤31-2x≤39, which of the following represents all possible values of x?

(A) -9≤x≤4
(B) -4≤x≤4
(C) -4≤x≤9
(D) 9≤x≤22
(E) 22≤x≤35

How should I go about doing this question, and what’s the quickest way? Thanks for your help!

Treat this just like it’s any equation, only instead of remembering to do any operations on both sides of the equals sign, you have to remember to do every operation to ALL THREE PARTS of the inequality.

First, subtract 31 from each part:

13 – 31 ≤ 31 – 2x – 31 ≤ 39 – 31
–18 ≤ –2x ≤ 8

Now divide by –2, remembering that when you multiply or divide a negative through an inequality, you need to flip the direction of the inequality:

9 ≥ x ≥ –4

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