Question

Which number line represents the solution set for the inequality –4(x + 3) ≤ –2 – 2x?

A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the left.
A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.

Answer 1

Solve: -4(x + 3) ≤ -2 - 2x
-4x - 12 ≤ -2 - 2x
-4x + 2x ≤ -2 + 12
-2x ≤ 10
x ≥ -5 (divide by -2, reverse inequality)

So the solution is x ≥ -5 — a closed dot at -5 with the ray pointing to the right. (Select the option showing a point at -5 with a bold line to the right.)