Question

question
graph the interval represented in inequality notation on the number line,
( x leq 2 ) or ( x geq 6 )

answer attempt 1 out of 3

number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12; text: click and drag to plot line

Explanation:

Step1: Analyze \( x \leq 2 \)

For \( x \leq 2 \), we use a closed circle at \( 2 \) (since the inequality is "less than or equal to") and shade to the left of \( 2 \) (towards negative infinity) on the number line.

Step2: Analyze \( x \geq 6 \)

For \( x \geq 6 \), we use a closed circle at \( 6 \) (since the inequality is "greater than or equal to") and shade to the right of \( 6 \) (towards positive infinity) on the number line.

Step3: Combine the two intervals

Since the inequality is "or", we combine the two shaded regions: the region to the left of and including \( 2 \), and the region to the right of and including \( 6 \).

To graph this:

1. Place a closed dot at \( 2 \) and draw a line (with an arrow) to the left (covering all numbers \( \leq 2 \)).
2. Place a closed dot at \( 6 \) and draw a line (with an arrow) to the right (covering all numbers \( \geq 6 \)).

Answer:

• For \( x \leq 2 \): Closed circle at \( 2 \), shade left.
• For \( x \geq 6 \): Closed circle at \( 6 \), shade right.

(Visually, on the given number line, mark a closed dot at \( 2 \) and draw a segment with an arrow to the left, and mark a closed dot at \( 6 \) and draw a segment with an arrow to the right.)