Graph Basic Inequalities on Number Lines (A) - Free Printable

Let’s go through each inequality one by one and figure out how to graph it on the number line.

We’ll use these rules:
- If the inequality is < or >, we use an open circle (○) at the number — meaning that number is NOT included.
- If the inequality is ≤ or ≥, we use a closed circle (●) — meaning that number IS included.
- Then, we shade the part of the number line that makes the inequality true:
- For “less than” (< or ≤), shade to the left.
- For “greater than” (> or ≥), shade to the right.

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1. x < 1

- This means all numbers less than 1.
- Since it’s “<”, we use an open circle at 1.
- Shade everything to the left of 1.

✔ Graph: Open circle at 1, arrow/shading going left toward -∞.

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2. x ≥ -6

- This means all numbers greater than or equal to -6.
- Since it’s “≥”, we use a closed circle at -6.
- Shade everything to the right of -6.

✔ Graph: Closed circle at -6, arrow/shading going right toward +∞.

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3. x ≥ 4

- All numbers greater than or equal to 4.
- Closed circle at 4.
- Shade to the right.

✔ Graph: Closed circle at 4, shading right.

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4. x ≥ 8

- All numbers greater than or equal to 8.
- Closed circle at 8.
- Shade to the right.

✔ Graph: Closed circle at 8, shading right.

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5. x ≤ 1

- All numbers less than or equal to 1.
- Closed circle at 1 (because of “≤”).
- Shade to the left.

✔ Graph: Closed circle at 1, shading left.

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Final Answer:

1. Open circle at 1, shaded left
2. Closed circle at -6, shaded right
3. Closed circle at 4, shaded right
4. Closed circle at 8, shaded right
5. Closed circle at 1, shaded left