Question

graph the compound inequality on the number line. ( x geq 4 ) or ( x < -8 )

Explanation:

Step1: Analyze \( x \geq 4 \)

For \( x \geq 4 \), we use a closed dot at \( 4 \) (since \( x \) can equal \( 4 \)) and draw an arrow to the right (because \( x \) is greater than or equal to \( 4 \)).

Step2: Analyze \( x < -8 \)

For \( x < -8 \), we use an open dot at \( -8 \) (since \( x \) cannot equal \( -8 \)) and draw an arrow to the left (because \( x \) is less than \( -8 \)).

Step3: Combine the two graphs

On the number line, mark a closed dot at \( 4 \) and draw an arrow to the right. Then, mark an open dot at \( -8 \) and draw an arrow to the left.

Answer:

• For \( x \geq 4 \): Closed dot at \( 4 \), arrow right.
• For \( x < -8 \): Open dot at \( -8 \), arrow left. (Graphically, on the given number line, place a closed circle at \( 4 \) with a line extending to the right, and an open circle at \( -8 \) with a line extending to the left.)