Which of the following describes all values of x that satisfy −7

Question

Which of the following describes all values of x that satisfy −7 < 3 − 2x ≤ 5?

Accepted Answer

A. −1 ≤ x < 5. Subtract 3 throughout: −10 < −2x ≤ 2. Divide by −2 and flip both signs: 5 > x ≥ −1, that is, −1 ≤ x < 5.

Answer

B. −1 < x ≤ 5 — The ≤ and < are on the wrong ends: dividing by −2 flips which end is inclusive.

Answer

C. −5 < x ≤ 1 — The endpoints were not divided by −2 correctly (−10 ÷ −2 = 5, 2 ÷ −2 = −1).

Answer

D. 1 ≤ x < 5 — 1 ≤ x < 5 uses the wrong sign on the lower endpoint.

Algebra practice question