Question

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

Explanation:

Step1: Analyze \( x < 4 \)

For the inequality \( x < 4 \), we use an open circle at \( 4 \) (since \( x \) is not equal to \( 4 \)) and draw an arrow to the left (towards negative infinity) to represent all numbers less than \( 4 \).

Step2: Analyze \( x > 8 \)

For the inequality \( x > 8 \), we use an open circle at \( 8 \) (since \( x \) is not equal to \( 8 \)) and draw an arrow to the right (towards positive infinity) to represent all numbers greater than \( 8 \).

Answer:

To graph \( x < 4 \) or \( x > 8 \) on the number line:

1. For \( x < 4 \): Place an open circle at \( 4 \) and draw a line with an arrow pointing to the left (covering all numbers less than \( 4 \)).
2. For \( x > 8 \): Place an open circle at \( 8 \) and draw a line with an arrow pointing to the right (covering all numbers greater than \( 8 \)).

(Visually, on the given number line, the open circle at \( 4 \) with left - arrow and open circle at \( 8 \) with right - arrow represent the solution set of the compound inequality.)