Illustrate the set on a number line.

StartSet z | z less than or equals 5 EndSet{z | z≤5}

To illustrate the set \(\{z \mid z \leq 5\}\) on a number line:

1. Draw a horizontal line representing the number line.
2. Mark the number 5 on the line.
3. Use a filled circle (●) on 5 to indicate that \(z = 5\) is included in the set (since \(z \leq 5\)).
4. Shade or darken the portion of the line to the left of 5, extending to negative infinity (since the set includes all numbers less than or equal to 5).

Here's a visual description of the number line:

- The number line has a filled circle at 5, and everything to the left of 5 is shaded.

Would you like me to generate a drawing to go along with this explanation?

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Here are five related questions to think about:
1. How would the graph change if the set were \(\{z \mid z < 5\}\)?
2. How would you represent \(\{z \mid z \geq -3\}\) on a number line?
3. What is the difference between an open circle and a closed circle on a number line?
4. How do you represent the set \(\{z \mid z \neq 3\}\) on a number line?
5. What is the union of \(\{z \mid z \leq 5\}\) and \(\{z \mid z > 7\}\) on a number line?

**Tip:** When graphing inequalities on a number line, a closed circle represents inclusion (≤ or ≥), and an open circle represents exclusion (< or >).

Illustrate the set on a number line. StartSet z | z less than or equals 5 EndSet{z | z≤5}

Learn how to illustrate the set {z | z ≤ 5} on a number line. This tutorial covers key concepts like inequalities, set notation, and graphing on a number line, suitable for students in Grades 6-8.

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