Equations and inequalities · Ages 14–15
Linear inequalities in one unknown worksheet
Covers: Inequalities and the number line, Properties of inequalities, Solving linear inequalities, Compound inequalities: and, or, Word problems with inequalities
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Linear inequalities in one unknown worksheet
Equations and inequalities · Ages 14–15
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.x is a positive whole number and x < 4. How many values can x take?
Answer:
2.The number line shows the solutions of an inequality. The least whole-number solution is
Answer:
3.−1 > −2. After both sides are multiplied by 2, the bigger of the two products is
Answer:
4.Solve 5x − 6 ≥ 9: x ≥
Answer:
5.How many whole-number solutions has −1 < x ≤ 6?
Answer:
6.5 times a number, take away 6, is not less than 45. What is the least whole number it can be?
Answer:
Part B: Choose, or true or false (2 marks each)
7.Which inequality has the same solutions as 3 ≥ x?
- A. x ≥ 3
- B. x ≤ 3
- C. x > 3
- D. x < 3
Choose the right answer
Answer:
8.If a < b, which of these must be true?
- A. a + 3 < b + 3
- B. a ÷ 3 > b ÷ 3
- C. a − 3 > b − 3
- D. −3a < −3b
Choose the right answer
Answer:
9.If x > y, then −4x > −4y.
True or false?
Answer:
10.What is the solution of 9x + 5 < 59?
- A. x < −6
- B. x < 6
- C. x > 6
- D. x ≤ 6
Choose the right answer
Answer:
11.What is the solution of x > 0 and x ≤ 5?
- A. x > 0
- B. 0 ≤ x < 5
- C. 0 < x ≤ 5
- D. x ≤ 5
Choose the right answer
Answer:
12.A lift's sign says "no more than 16 passengers". With x passengers, how is that written as an inequality?
- A. x ≤ 16
- B. x ≥ 16
- C. x < 16
- D. x > 16
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A car park's entrance has a 1.9 m height limit: a vehicle's height h ≤ 1.9. A car 1.5 m high can be raised by at most m; another, 2.4 m high, must come down by at least m to get in.
Fill in each blank
Working:
Answer:
14.A ride's rule says "at least 128 cm tall to ride". With a height of h cm, which inequality shows the heights that may ride?
- A. h < 128
- B. h ≤ 128
- C. h ≥ 128
- D. h > 128
Choose the right answer
Working:
Answer:
15.Tower A is 800 m tall, taller than tower B's 200 m: 800 > 200. Models of both are made at 1 : 100 (both sides divided by 100): A's model is m tall and B's m, A's still the taller.
Fill in each blank
Working:
Answer:
16.A rectangular flower bed is 19 m long, and there is fencing for only 52 m, so its perimeter can't be more than 52 m. With a width of x m: 2(19 + x) ≤ 52, 19 + x ≤ , x ≤ .
Fill in each blank
Working:
Answer:
17.A pool's water must be warmer than 28°C and no warmer than 31°C. In whole degrees, how many temperatures fit?
Working:
Answer:
18.A lift takes at most 900 kg. 5 passengers weigh 325 kg in all, and boxes of 19 kg each go in too. With x boxes: 325 + 19x ≤ 900, 19x ≤ , so at most boxes can go in.
Fill in each blank
Working:
Answer:
Show the answers and working
Linear inequalities in one unknown worksheet: Answers and working
Part A: Working out and filling in
1. 3
Positive whole numbers start at 1, and x < 4 leaves 4 out: 1, 2, …, 3, which is 3 of them.
2. 7
The line runs right from 6: filled, 6 itself is a solution; hollow, 6 is left out and the least whole number is the next one. Here it is 7.
3. −2
−1 × (2) = −2 and −2 × (2) = −4. Times a negative, the side that was smaller becomes the bigger.
4. 3
Take −6 from both sides: 5x ≥ 9 − (−6) = 15; divide both sides by the positive 5, the sign staying: x ≥ 3.
5. 7
−1 out, 6 in: from the number after −1 up to 6, that is 6 − (−1) = 7 of them.
6. 11
With the number x: 5x − 6 ≥ 45, 5x ≥ 51, x ≥ 515. The least whole number from there is 11.
Part B: Choose, or true or false
7. B. x ≤ 3
Swap the two sides and the sign turns round with them: 3 ≥ x is x ≤ 3. Check by putting numbers in: x = 3 gives 3 ≥ 3, true, while anything bigger than 3 fails.
8. A. a + 3 < b + 3
Adding the same number, 3, to both sides keeps the sign as it is.
9. False
Both sides times a positive number: the sign stays; times a negative: it turns. Try x = 4, y = 0: compare −4 × 4 with 0.
10. B. x < 6
9x < 59 − (5), so 9x < 9 × 6; divide by 9: x < 6.
11. C. 0 < x ≤ 5
"And" takes where the two overlap: above 0 and not above 5, that is 0 < x ≤ 5.
12. A. x ≤ 16
"No more than 16" is at most 16: x ≤ 16.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 0.4, 0.5
h ≤ 1.9 takes in exactly 1.9 m: 1.9 − 1.5 = 0.4; 2.4 − 1.9 = 0.5.
14. C. h ≥ 128
"At least 128 cm" is greater than or equal to 128: h ≥ 128.
15. 8, 2
800 ÷ 100 = 8 and 200 ÷ 100 = 2: dividing by a positive number keeps the sign, 8 > 2.
16. 26, 7
Halve both sides: 19 + x ≤ 26; take away 19: x ≤ 7. The bed is at most 7 m wide.
17. 3 temperatures
x > 28 and x ≤ 31, that is 28 < x ≤ 31: 28 out, 31 in, so 31 − 28 = 3 of them.
18. 575, 30
19x ≤ 900 − 325 = 575, x ≤ 57519. Boxes are whole, so round down: at most 30.
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