Question

Choose the correct description of the graph of the compound inequality

x - 2 > -10 and 2x 12

A number line with an open circle on -8, a closed circle on 6, and shading in between.

A number line with an open circle on -8, shading to the left, and a closed circle on 6, shading to the right.

A number line with a closed circle on -8, shading to the left, and an open circle on 6, shading to the right.

A number line with a closed circle on -8, an open circle on 6, and shading in between.

Answer 1

\[\le \]

Answer 2

Since your question has an "and", you are looking for an intersection, so your shading will be continuous, that is, not broken up into 2 parts.

The first inequality resolves down to:

x > -8

and that is achieved by adding 2 to both sides (and keeping the sign the same). So the shading there looks like an open circle on -8 and shading to the right.

The second inequality is already simplified so it is a closed circle (because of the equal) on 6 and shading to the left. That is gotten by dividing both sides by 2 (and again keeping the sign the same).

The intersection is represented by:

"A" your first choice

shading in between.