Question

Which graph represents the solution set of the compound inequality below?

x + 3 < (4x – 12) < 20

A number line with an open circle at 5 with a bold line pointing to the left and an open circle at 8 with a bold line pointing to the right.
A number line with an open circle at 5 with a bold line pointing to the right stopping at the open circle at 8.
A number line with an open circle at 9 with a bold line pointing to the left and an open circle at 13 with a bold line pointing to the right.
A number line with an open circle at 9 with a bold line pointing to the right stopping at the open circle at 13.

Answer 1

Solve each part:

x + 3 < 4x − 12 => 15 < 3x => x > 5
4x − 12 < 20 => 4x < 32 => x < 8

So 5 < x < 8. That is the number line with an open circle at 5 and an open circle at 8 with a bold line between them (the second option).