Question

Choose the correct description of the graph of the compound inequality:

X - 3 < -9 or x + 5 ≥ 10.
A) A number line with an open circle on -6, shading to the left, and a closed circle on 5, shading to the right.
B) A number line with a closed circle on -6, shading to the left, and an open circle on 5, shading to the right.
C) A number line with an open circle on -6, a closed circle on 5, and shading in between.
D) A number line with a closed circle on -6, an open circle on 5, and shading in between.

Answer 1

The correct graph of the compound inequality x - 3 < -9 or x + 5 ≥ 10 depicts a number line with an open circle on -6 (shading left) and a closed circle on 5 (shading right), which corresponds to choice A.

Step-by-step explanation:

To choose the correct description of the graph of the compound inequality x - 3 < -9 or x + 5 ≥ 10, we first solve each inequality separately.

For x - 3 < -9:

1. Add 3 to both sides to get x < -6.

For x + 5 ≥ 10:

1. Subtract 5 from both sides to get x ≥ 5.

The compound inequality means we consider where either of these conditions is met. The first inequality represents all numbers to the left of -6 (not including -6 itself, indicated by an open circle), and the second inequality represents all numbers to the right of 5 (including 5 itself, indicated by a closed circle). These two sets of numbers do not overlap, so the graph is of two separate portions of the number line.

The correct description is A) A number line with an open circle on -6, shading to the left, and a closed circle on 5, shading to the right.