Inequalities Worksheets with Answer Key - Free Printable

Let’s solve each inequality one by one. We’ll find which numbers from the given choices make the inequality true.

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Problem 1: 2x ≥ 8

We need to find values of x that make this true.

Divide both sides by 2 → x ≥ 4

Given choices: 1, 3, 4, 6

Check:
- 1 → 2×1 = 2 → not ≥ 8 ✘
- 3 → 2×3 = 6 → not ≥ 8 ✘
- 4 → 2×4 = 8 → yes ✔
- 6 → 2×6 = 12 → yes ✔

✔ Circle: 4, 6

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Problem 2: x – 3 < 9

Add 3 to both sides → x < 12

Choices: 16, 5, 18, 10

Check:
- 16 → 16–3=13 → not < 9 ✘
- 5 → 5–3=2 → yes ✔
- 18 → 18–3=15 → no ✘
- 10 → 10–3=7 → yes ✔

✔ Circle: 5, 10

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Problem 3: 12 > x + 6

Subtract 6 from both sides → 6 > x → or x < 6

Choices: 2, 3, 6, 5

Check:
- 2 → 2+6=8 → 12>8? Yes ✔
- 3 → 3+6=9 → 12>9? Yes ✔
- 6 → 6+6=12 → 12>12? No (equal) ✘
- 5 → 5+6=11 → 12>11? Yes ✔

✔ Circle: 2, 3, 5

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Problem 4: x/2 > 9

Multiply both sides by 2 → x > 18

Choices: 2, 20, 6, 8

Only 20 is greater than 18.

✔ Circle: 20

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Problem 5: 5x ≤ 10

Divide by 5 → x ≤ 2

Choices: 5, 1, 2, 4

Check:
- 5 → 5×5=25 → too big ✘
- 1 → 5×1=5 → ≤10 ✔
- 2 → 5×2=10 → ≤10 ✔
- 4 → 5×4=20 → too big ✘

✔ Circle: 1, 2

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Problem 6: x + 5 > 9

Subtract 5 → x > 4

Choices: 2, 1, 7, 9

Check:
- 2 → 2+5=7 → not >9 ✘
- 1 → 1+5=6 → no ✘
- 7 → 7+5=12 → yes ✔
- 9 → 9+5=14 → yes ✔

✔ Circle: 7, 9

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Problem 7: x + 7 ≥ 14

Subtract 7 → x ≥ 7

Choices: 3, 11, 5, 7

Check:
- 3 → 3+7=10 → no ✘
- 11 → 11+7=18 → yes ✔
- 5 → 5+7=12 → no ✘
- 7 → 7+7=14 → yes ✔

✔ Circle: 11, 7

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Problem 8: x/3 < 5

Multiply by 3 → x < 15

Choices: 17, 12, 6, 16

Check:
- 17 → 17/3 ≈ 5.67 → not <5 ✘
- 12 → 12/3=4 → <5 ✔
- 6 → 6/3=2 → <5 ✔
- 16 → 16/3≈5.33 → not <5 ✘

✔ Circle: 12, 6

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Problem 9: 16 > x + 7

Subtract 7 → 9 > x → x < 9

Choices: 8, 10, 15, 12

Check:
- 8 → 8+7=15 → 16>15? Yes ✔
- 10 → 10+7=17 → 16>17? No ✘
- 15 → 15+7=22 → no ✘
- 12 → 12+7=19 → no ✘

✔ Circle: 8

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Problem 10: 5 > x/5

Multiply both sides by 5 → 25 > x → x < 25

Choices: 20, 25, 5, 15

Check:
- 20 → 20/5=4 → 5>4? Yes ✔
- 25 → 25/5=5 → 5>5? No ✘
- 5 → 5/5=1 → 5>1? Yes ✔
- 15 → 15/5=3 → 5>3? Yes ✔

✔ Circle: 20, 5, 15

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Problem 11: 6x ≤ 18

Divide by 6 → x ≤ 3

Choices: 5, 4, 3, 2

Check:
- 5 → 6×5=30 → too big ✘
- 4 → 6×4=24 → too big ✘
- 3 → 6×3=18 → ≤18 ✔
- 2 → 6×2=12 → ≤18 ✔

✔ Circle: 3, 2

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Problem 12: 20 ≥ 2x

Divide by 2 → 10 ≥ x → x ≤ 10

Choices: 13, 10, 9, 8

Check:
- 13 → 2×13=26 → 20≥26? No ✘
- 10 → 2×10=20 → 20≥20? Yes ✔
- 9 → 2×9=18 → 20≥18? Yes ✔
- 8 → 2×8=16 → 20≥16? Yes ✔

✔ Circle: 10, 9, 8

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Final Answer:

1. 4, 6
2. 5, 10
3. 2, 3, 5
4. 20
5. 1, 2
6. 7, 9
7. 11, 7
8. 12, 6
9. 8
10. 20, 5, 15
11. 3, 2
12. 10, 9, 8