Question

graph the compound inequality on the number line.
$x < -7$ or $x > -5$

Explanation:

Step1: Analyze \( x < -7 \)

For the inequality \( x < -7 \), we use an open circle at \( -7 \) (since \( x \) is not equal to \( -7 \)) and draw an arrow to the left (indicating all numbers less than \( -7 \)).

Step2: Analyze \( x > -5 \)

For the inequality \( x > -5 \), we use an open circle at \( -5 \) (since \( x \) is not equal to \( -5 \)) and draw an arrow to the right (indicating all numbers greater than \( -5 \)).

Step3: Combine the two graphs

On the number line provided, place an open circle at \( -7 \) and draw an arrow to the left, and place an open circle at \( -5 \) and draw an arrow to the right.

(Note: Since the actual drawing is done using the provided tools, the key is to identify the correct points and directions. The open circles are used because the inequalities are strict (\( < \) and \( > \), not \( \leq \) or \( \geq \)).)

Answer:

To graph \( x < -7 \) or \( x > -5 \):

1. For \( x < -7 \): Place an open circle at \( -7 \) (on the number line) and draw an arrow to the left (toward \( -10, -9, \dots \)).
2. For \( x > -5 \): Place an open circle at \( -5 \) (on the number line) and draw an arrow to the right (toward \( -4, -3, \dots, 10 \)).

(Use the "open circle" (\( \circ \)) tool for \( -7 \) and \( -5 \), and the "arrow" tool to extend left from \( -7 \) and right from \( -5 \).)