Let’s solve each inequality one by one. We’ll isolate the variable on one side, just like solving equations — but remember: if you multiply or divide by a negative number, flip the inequality sign!
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1. –6 + 7x > –2
Add 6 to both sides:
→ 7x > 4
Divide by 7:
→ x > 4/7
✔ Final Answer for #1:
x > 4/7
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2. 7 ≥ –8z + 7
Subtract 7 from both sides:
→ 0 ≥ –8z
Divide by –8 → FLIP the sign!
→ 0 ≤ z (or z ≥ 0)
✔ Final Answer for #2:
z ≥ 0
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3. 7 ≥ –9 + 5c
Add 9 to both sides:
→ 16 ≥ 5c
Divide by 5:
→ 16/5 ≥ c (or c ≤ 16/5)
✔ Final Answer for #3:
c ≤ 16/5
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4. –8 < –9n + 9
Subtract 9 from both sides:
→ –17 < –9n
Divide by –9 → FLIP the sign!
→ 17/9 > n (or n < 17/9)
✔ Final Answer for #4:
n < 17/9
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5. 7 ≥ 8 – 8w
Subtract 8 from both sides:
→ –1 ≥ –8w
Divide by –8 → FLIP the sign!
→ 1/8 ≤ w (or w ≥ 1/8)
✔ Final Answer for #5:
w ≥ 1/8
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6. 7 ≥ –4z + 7
Subtract 7 from both sides:
→ 0 ≥ –4z
Divide by –4 → FLIP the sign!
→ 0 ≤ z (or z ≥ 0)
✔ Final Answer for #6:
z ≥ 0
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7. 2 – f > 3
Subtract 2 from both sides:
→ –f > 1
Multiply by –1 → FLIP the sign!
→ f < –1
✔ Final Answer for #7:
f < –1
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8. –5 < –7 + 4f
Add 7 to both sides:
→ 2 < 4f
Divide by 4:
→ 1/2 < f (or f > 1/2)
✔ Final Answer for #8:
f > 1/2
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9. –1 > 6 – 2f
Subtract 6 from both sides:
→ –7 > –2f
Divide by –2 → FLIP the sign!
→ 7/2 < f (or f > 7/2)
✔ Final Answer for #9:
f > 7/2
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10. –5w – 2 ≤ 1
Add 2 to both sides:
→ –5w ≤ 3
Divide by –5 → FLIP the sign!
→ w ≥ –3/5
✔ Final Answer for #10:
w ≥ –3/5
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Final Answer:
1. x > 4/7
2. z ≥ 0
3. c ≤ 16/5
4. n < 17/9
5. w ≥ 1/8
6. z ≥ 0
7. f < –1
8. f > 1/2
9. f > 7/2
10. w ≥ –3/5
Parent Tip: Review the logic above to help your child master the concept of math worksheet on equations and inequalities.
