Let’s solve each inequality one by one. We’ll isolate the variable (x) and then graph the solution on a number line.
---
1. -2x < 8
Divide both sides by -2 → remember to flip the inequality sign when dividing by negative!
→ x > -4
Graph: Open circle at -4, arrow to the right.
---
2. -5 ≤ x/2
Multiply both sides by 2:
→ -10 ≤ x or x ≥ -10
Graph: Closed circle at -10, arrow to the right.
---
3. x/2 ≥ -3
Multiply both sides by 2:
→ x ≥ -6
Graph: Closed circle at -6, arrow to the right.
---
4. -1 > x/2
Multiply both sides by 2:
→ -2 > x or x < -2
Graph: Open circle at -2, arrow to the left.
---
5. -4x > 16
Divide both sides by -4 → flip the sign!
→ x < -4
Graph: Open circle at -4, arrow to the left.
---
6. x/(-3) ≥ 0
Multiply both sides by -3 → flip the sign!
→ x ≤ 0
Graph: Closed circle at 0, arrow to the left.
---
7. x/8 < -1
Multiply both sides by 8:
→ x < -8
Graph: Open circle at -8, arrow to the left.
---
8. 2 < x/(-5)
Multiply both sides by -5 → flip the sign!
→ -10 > x or x < -10
Graph: Open circle at -10, arrow to the left.
---
9. -12 ≤ 2x
Divide both sides by 2:
→ -6 ≤ x or x ≥ -6
Graph: Closed circle at -6, arrow to the right.
---
10. -4x > -8
Divide both sides by -4 → flip the sign!
→ x < 2
Graph: Open circle at 2, arrow to the left.
---
11. x/(-8) < -1
Multiply both sides by -8 → flip the sign!
→ x > 8
Graph: Open circle at 8, arrow to the right.
---
12. 16 ≤ -2x
Divide both sides by -2 → flip the sign!
→ -8 ≥ x or x ≤ -8
Graph: Closed circle at -8, arrow to the left.
---
Final Answer:
1. x > -4
2. x ≥ -10
3. x ≥ -6
4. x < -2
5. x < -4
6. x ≤ 0
7. x < -8
8. x < -10
9. x ≥ -6
10. x < 2
11. x > 8
12. x ≤ -8
Parent Tip: Review the logic above to help your child master the concept of solving one step inequalities worksheets.
