Question

make a graph on the number line that represents the inequality x ≤ 5.
-8 -6 -4 -2 0 2 4 6 8
click either side of the line

Explanation:

Step1: Analyze the inequality

The inequality is \( x \leq 5 \). This means we need to represent all real numbers less than or equal to 5 on the number line.

Step2: Determine the point and direction

• For \( x \leq 5 \), the critical point is 5. Since the inequality includes equality (\( \leq \)), we use a closed (filled) circle at 5.
• We need to shade (or indicate) all the numbers to the left of 5 (including 5) because we want values of \( x \) that are less than or equal to 5. In the given number line, we should click on the left side of the red dot (which should be moved to 5, but assuming the red dot is at 3 currently, we need to adjust the dot to 5 first and then shade left). Wait, looking at the number line, the red dot is at 3? Wait no, maybe the initial setup: the number line has marks at -8, -6, -4, -2, 0, 2, 4, 6, 8. Wait, the red dot is at 3? Wait no, the labels: between 2 and 4, the red dot is at 3? Wait, no, the inequality is \( x \leq 5 \), so the critical point is 5. So first, move the red dot to 5 (the position at 5 on the number line), then shade (or click) the left side of the dot (since \( x \leq 5 \) includes all numbers less than or equal to 5, so left of 5).

Wait, the current number line has a red dot at 3 (between 2 and 4), and a gray dot at 3? No, the gray dot is above the red dot. Wait, the task is to make the graph for \( x \leq 5 \). So:

1. Move the red dot to 5 (the position labeled 5 on the number line).
2. Since \( x \leq 5 \), we shade (or click) the left side of the dot (because all numbers less than or equal to 5 are to the left of 5 on the number line).

So the correct action is to place the closed circle at 5 and shade (click) the left side of the line at 5.

Answer:

To graph \( x \leq 5 \):

1. Place a closed (filled) circle at \( 5 \) on the number line (move the red dot to the position labeled \( 5 \)).
2. Click (shade) the left side of the circle (representing all values \( x \leq 5 \)).

(In the given interface, adjust the red dot to \( 5 \) and click the left side of the line at \( 5 \).)