Let’s solve each inequality one by one and graph them on the number line.
We’ll remember:
- For “<” or “>”, we use an
open circle (○) because the number itself is NOT included.
- For “≤” or “≥”, we use a
closed circle (●) because the number IS included.
- Then we shade the part of the number line that shows all numbers that make the inequality true.
---
1. x < 1
This means: all numbers less than 1.
→ Put an open circle at 1 (because 1 is not included).
→ Shade everything to the left (toward negative numbers).
Graph:
Open circle at 1, arrow going left.
---
2. x ≥ -6
This means: all numbers greater than or equal to -6.
→ Put a closed circle at -6 (because -6 is included).
→ Shade everything to the right (toward positive numbers).
Graph:
Closed circle at -6, arrow going right.
---
3. x ≥ 4
This means: all numbers greater than or equal to 4.
→ Closed circle at 4.
→ Shade to the right.
Graph:
Closed circle at 4, arrow going right.
---
4. x ≥ 8
This means: all numbers greater than or equal to 8.
→ Closed circle at 8.
→ Shade to the right.
Graph:
Closed circle at 8, arrow going right.
---
5. x ≤ 1
This means: all numbers less than or equal to 1.
→ Closed circle at 1 (because 1 is included).
→ Shade to the left.
Graph:
Closed circle at 1, arrow going left.
---
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.
Parent Tip: Review the logic above to help your child master the concept of writing and graphing inequalities worksheet.
