Equations and inequalities · Ages 14–15

Compound inequalities: and, or 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.

13.A delivery worker must take at least 3 boxes a trip. The trolley weighs 12 kg, each box 23 kg, and with its load it can't be over 273 kg. With x boxes: x ≥ 3 and 12 + 23x ≤ 273. x is at most , so there are numbers of boxes to choose from.
Fill in each blank
Working:
Answer:
14.A museum's cheaper ticket is only for people "under 8, or 63 and over". With an age of x years, which shows the ages that get it?
- A. x < 8 and x ≥ 63
- B. 8 ≤ x < 63
- C. x ≤ 8 or x > 63
- D. x < 8 or x ≥ 63
Choose the right answer
Working:
Answer:
15.A car park charges $26 an hour, in whole hours. Ming wants to pay more than $48 but no more than $173. How many different whole numbers of hours can he park for?
Working:
Answer:
16.A pool's water must be warmer than 24°C and no warmer than 28°C. In whole degrees, how many temperatures fit?
Working:
Answer:
17.A car park charges $28 an hour, in whole hours. Ming wants to pay more than $25 but no more than $141. How many different whole numbers of hours can he park for?
Working:
Answer:
18.A delivery worker must take at least 2 boxes a trip. The trolley weighs 14 kg, each box 16 kg, and with its load it can't be over 97 kg. With x boxes: x ≥ 2 and 14 + 16x ≤ 97. x is at most , so there are numbers of boxes to choose from.
Fill in each blank
Working:
Answer:

Show the answers and working

Compound inequalities: and, or worksheet: Answers and working

1. 3
−3 out, 0 in: from the number after −3 up to 0, that is 0 − (−3) = 3 of them.
2. 6
3 ≤ x ≤ 8, both ends in: 8 − (3) + 1 = 6 of them.
3. 8
−4 ≤ x ≤ 3, both ends in: 3 − (−4) + 1 = 8 of them.
4. 7
Solve each first: x > −2, x ≤ 5. They overlap in −2 < x ≤ 5: 5 − (−2) = 7 whole numbers.
5. 7
Solve each first: x > −3, x ≤ 4. They overlap in −3 < x ≤ 4: 4 − (−3) = 7 whole numbers.

6. D. 4 < x ≤ 8
"And" takes where the two overlap: above 4 and not above 8, that is 4 < x ≤ 8.
7. D. 1 ≤ x < 7
One is x ≥ 1, the other x < 7; they overlap in 1 ≤ x < 7.
8. A. x < 10
"Or" takes both together: x < 2 lies inside x < 10, so together they are x < 10.
9. True
Draw both on a number line: x > −4 runs right, x < −7 runs left. They have solutions only if they overlap, that is if −4 < −7.
10. False
Draw both on a number line: x > 3 runs right, x < 5 runs left. They have solutions only if they overlap, that is if 3 < 5.
11. B. Every number
x ≤ 4 runs left and x > 1 runs right, with 1 < 4: together they cover the whole line, so every number is a solution.
12. B. Every number
x ≤ 2 runs left and x > 1 runs right, with 1 < 2: together they cover the whole line, so every number is a solution.

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

13. 11, 9
23x ≤ 273 − 12, so x is at most 11, a whole number. x can be 3 to 11: 11 − 3 + 1 = 9 choices.
14. D. x < 8 or x ≥ 63
Fitting either one is enough: x < 8 or x ≥ 63.
15. 5 of them
With x hours: 26x > 48 and 26x ≤ 173, that is 4826 < x ≤ 17326. Count the whole numbers in that stretch: 5.
16. 4 temperatures
x > 24 and x ≤ 28, that is 24 < x ≤ 28: 24 out, 28 in, so 28 − 24 = 4 of them.
17. 5 of them
With x hours: 28x > 25 and 28x ≤ 141, that is 2528 < x ≤ 14128. Count the whole numbers in that stretch: 5.
18. 5, 4
16x ≤ 97 − 14, so x is at most 5, a whole number. x can be 2 to 5: 5 − 2 + 1 = 4 choices.

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