Equations and inequalities · Ages 14–15

Inequalities and the number line worksheet

Part of: Linear inequalities in one unknown

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Equations and inequalities · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.x is a positive whole number and x < 10. How many values can x take?
Answer:
2.The number line shows the solutions of an inequality. The least whole-number solution is
Answer:

13.A ride's rule says "at least 110 cm tall to ride". With a height of h cm, which inequality shows the heights that may ride?
- A. h < 110
- B. h > 110
- C. h ≤ 110
- D. h ≥ 110
Choose the right answer
Working:
Answer:
14.Frozen food must be kept colder than −2°C. With a temperature of x°C, which number line shows the temperatures it can be kept at?
- A
- B
- C
- D
Choose the right picture
Working:
Answer:
15.A car park's entrance has a 1.9 m height limit: a vehicle's height h ≤ 1.9. A car 1.6 m high can be raised by at most m; another, 2.3 m high, must come down by at least m to get in.
Fill in each blank
Working:
Answer:
16.A medicine must be kept no warmer than 4°C, that is at a temperature T ≤ 4. Four fridges are at 4°C, 1°C, 4°C and 5°C. How many of them can keep it?
Working:
Answer:
17."Applicants must be 15 or over": with an age of x years, the condition to apply is written x ≥ 15.
True or false?
Working:
Answer:
18.A ride's rule says "at least 135 cm tall to ride". With a height of h cm, which inequality shows the heights that may ride?
- A. h ≥ 135
- B. h > 135
- C. h < 135
- D. h ≤ 135
Choose the right answer
Working:
Answer:

Show the answers and working

Inequalities and the number line worksheet: Answers and working

1. 9
Positive whole numbers start at 1, and x < 10 leaves 10 out: 1, 2, …, 9, which is 9 of them.
2. 3
The line runs right from 2: filled, 2 itself is a solution; hollow, 2 is left out and the least whole number is the next one. Here it is 3.

3. True
x ≤ 4 takes in 4 and every number smaller. Put in x = 2.5 and see whether 2.5 ≤ 4 holds.
4. True
The solutions of x > −6 are all the numbers bigger than −6 (−6 itself left out). Put in x = −4 and see whether −4 > −6 is true.
5. D. x ≤ 2
Look at two things: is the circle hollow (2 left out) or filled (2 in), and does the line run right (greater) or left (less)?
6. A. x ≤ 19
"At most", "not greater than" and "not over" are all ≤: equal to 19 or less.
7. A. x ≤ −3
"At most", "not greater than" and "not over" are all ≤: equal to −3 or less.
8. False
The solutions of x > 4 are all the numbers bigger than 4 (4 itself left out). Put in x = 3 and see whether 3 > 4 is true.
9. D. x ≥ 10
Not less than 10 is greater than or equal to 10: x ≥ 10, the same as "at least 10".
10. B
≤ takes 2 in, so the circle is filled; less than runs left.
11. C
≤ takes 3 in, so the circle is filled; less than runs left.
12. A. x ≤ −9
Swap the two sides and the sign turns round with them: −9 ≥ x is x ≤ −9. Check by putting numbers in: x = −9 gives −9 ≥ −9, true, while anything bigger than −9 fails.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. D. h ≥ 110
"At least 110 cm" is greater than or equal to 110: h ≥ 110.
14. A
Colder than −2°C: x < −2, a hollow circle at −2, running left.
15. 0.3, 0.4
h ≤ 1.9 takes in exactly 1.9 m: 1.9 − 1.6 = 0.3; 2.3 − 1.9 = 0.4.
16. 3 fridges
Try each in T ≤ 4: exactly 4 is fine, anything warmer isn't. That is 3 of them.
17. True
15 or over means 15 or more: x ≥ 15.
18. A. h ≥ 135
"At least 135 cm" is greater than or equal to 135: h ≥ 135.

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