Question

Which graph represents the solution to the compound inequality?

–2x + 4 ≤ 8 and –2x + 4 > –6

A number line with a point at negative 2 with a bold line pointing to the right ending at the open circle at 5.
A number line with an open circle at negative 2 with a bold line pointing to the right ending at the point at negative 5.
A number line with a point at negative 2 with a bold line pointing to the left. An open circle at 5 with a bold line pointing to the right.
A number line with an open circle at negative 2 with a bold line pointing to the left. A point at 5 with a bold line pointing to the right.

Answer 1

Solve each inequality:

–2x + 4 ≤ 8 → –2x ≤ 4 → x ≥ –2.

–2x + 4 > –6 → –2x > –10 → x < 5.

Combine: x ≥ –2 and x < 5 → interval [–2, 5). That is a closed dot at –2, open circle at 5, with the segment between them shaded. Matches the first description.