Solutions to Inequalities | Interactive Worksheet - Free Printable

Let’s go through each inequality one by one and check which listed values satisfy it.

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1. a > 6
We need numbers greater than 6.
Given: a = 1, 6, 7, 16
→ 7 > 6 ✔
→ 16 > 6 ✔
→ 6 is not greater than 6 ✘
→ 1 is not > 6 ✘
✔ Solutions: a = 7, 16

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2. x < 3
Numbers less than 3.
Given: x = 2, 3, 7, 9
→ 2 < 3 ✔
→ 3 is not less than 3 ✘
→ 7, 9 are too big
✔ Solution: x = 2

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3. r ≤ 10
Less than or equal to 10.
Given: r = 5, 10, 15, 20
→ 5 ≤ 10 ✔
→ 10 ≤ 10 ✔
→ 15, 20 are too big ✘
✔ Solutions: r = 5, 10

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4. 14 ≤ c
Same as c ≥ 14 → c must be 14 or more.
Given: c = 11, 14, 15, 17
→ 11 < 14 ✘
→ 14 ≥ 14 ✔
→ 15 ≥ 14 ✔
→ 17 ≥ 14 ✔
✔ Solutions: c = 14, 15, 17

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5. y ≥ 15
y must be 15 or more.
Given: y = 0, 9, 14, 15
→ 0, 9, 14 are all less than 15 ✘
→ 15 ≥ 15 ✔
✔ Solution: y = 15

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6. 13 > n
Same as n < 13
Given: n = 2, 11, 13, 28
→ 2 < 13 ✔
→ 11 < 13 ✔
→ 13 is not less than 13 ✘
→ 28 is way too big ✘
✔ Solutions: n = 2, 11

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7. m + 7 > 11
Subtract 7 from both sides: m > 4
Given: m = 4, 8, 10, 11
→ 4 > 4? No ✘
→ 8 > 4 ✔
→ 10 > 4 ✔
→ 11 > 4 ✔
✔ Solutions: m = 8, 10, 11

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8. z - 12 < 8
Add 12 to both sides: z < 20
Given: z = 12, 14, 20, 25
→ 12 < 20 ✔
→ 14 < 20 ✔
→ 20 is not less than 20 ✘
→ 25 > 20 ✘
✔ Solutions: z = 12, 14

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9. (2/5)y > 9
Multiply both sides by 5: 2y > 45
Divide by 2: y > 22.5
So y must be greater than 22.5
Given: y = 9, 20, 45, 100
→ 9 < 22.5 ✘
→ 20 < 22.5 ✘
→ 45 > 22.5 ✔
→ 100 > 22.5 ✔
✔ Solutions: y = 45, 100

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10. 44 ≥ 2n
Divide both sides by 2: 22 ≥ n → n ≤ 22
Given: n = 3, 13, 22, 44
→ 3 ≤ 22 ✔
→ 13 ≤ 22 ✔
→ 22 ≤ 22 ✔
→ 44 > 22 ✘
✔ Solutions: n = 3, 13, 22

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Final Answer:
- a > 6 → a = 7, 16
- x < 3 → x = 2
- r ≤ 10 → r = 5, 10
- 14 ≤ c → c = 14, 15, 17
- y ≥ 15 → y = 15
- 13 > n → n = 2, 11
- m + 7 > 11 → m = 8, 10, 11
- z - 12 < 8 → z = 12, 14
- (2/5)y > 9 → y = 45, 100
- 44 ≥ 2n → n = 3, 13, 22