Question

graph the inequality below on the number line.
x ≤ 4

Explanation:

Step1: Understand the inequality

The inequality is \( x \leq 4 \). This means we need to represent all real numbers less than or equal to 4 on the number line.

Step2: Identify the critical point

The critical point here is 4. Since the inequality is "less than or equal to", we will use a closed (filled) circle at 4 to indicate that 4 is included in the solution set.

Step3: Determine the direction of the line

For \( x \leq 4 \), the solutions are all numbers to the left of 4 (including 4 itself). So we draw a line starting from the closed circle at 4 and extending to the left (towards negative infinity) on the number line.

To graph it:

1. Locate the number 4 on the number line.
2. Place a closed circle (because the inequality is \( \leq \), so 4 is included) at 4.
3. Draw an arrow starting from the closed circle at 4 and going to the left (towards smaller numbers) to represent all numbers less than or equal to 4.

Answer:

To graph \( x \leq 4 \) on the number line:

• Put a closed (filled) circle at 4 (since 4 is included in the solution set because of the "≤" symbol).
• Draw a line with an arrow pointing to the left from the closed circle at 4 to represent all numbers less than or equal to 4.