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Inequalities practice questions with answers

Foundation and Higher · Grade 4 · Non-calculator

A second set of inequalities questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Solve 3x − 2 < 7.

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Answer: x<3

  1. Add 2, then divide by 3.
  2. The value is x<3.
  • Method (1): Add 2, then divide by 3.
  • Accuracy (1): Answer x<3

Question 2 Easy

Solve 2x ≤ 10.

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Answer: x≤5

  1. Divide both sides by 2.
  2. The value is x≤5.
  • Method (1): Divide both sides by 2.
  • Accuracy (1): Answer x≤5

Question 3 Medium

List the integers x with 0 < x < 4. Give them in order, separated by commas.

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Answer: 1, 2, 3

  1. x is greater than 0 and less than the bound.
  2. Keep only the whole numbers in between.
  • Method (1): x is greater than 0 and less than the bound.
  • Accuracy (1): Answer 1, 2, 3

Question 4 Medium

The inequality is x ≥ 2. What is the smallest integer solution?

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Answer: 2

  1. The bound is included.
  2. The smallest integer is 2.
  • Method (1): The bound is included.
  • Accuracy (1): Answer 2

Question 5 Hard

Twice a number, minus 1, is less than 11. What is the largest integer the number can be?

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Answer: 5

  1. 2x < 12.
  2. The largest integer below that bound is 5.
  • Method (1): 2x < 12.
  • Accuracy (1): Answer 5

Question 6 Hard

Solve −3x ≤ 6.

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Answer: x≥-2

  1. Divide by −3.
  2. The inequality sign reverses.
  • Method (1): Divide by −3.
  • Accuracy (1): Answer x≥-2

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

A number x is multiplied by 3, then 4 is added, and the result is at least 16. Solve for x.

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Answer: x≥4

  1. 3x + 4 is at least the total.
  2. Subtract 4 and divide by 3.
  • Method (1): 3x + 4 is at least the total.
  • Accuracy (1): Answer x≥4

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Solve 2x − 6 > 10.

  1. x>8
  2. x<8
  3. x>5
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x>8 The result is x>8.

Check 2

Solve 10 − 3x ≤ 4.

  1. x≥2
  2. x≤2
  3. x≥-2
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x≥2 The result is x≥2.

Check 3

x is a whole number and 2x + 1 < 8. What is the largest possible value of x?

  1. 3
  2. 4
  3. 3.5
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3 The result is 3.

Check 4

How many whole numbers satisfy 3 < x ≤ 10?

  1. 7
  2. 8
  3. 9
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7 The result is 7.

Check 5

Solve 2x − 2 ≤ 2.

  1. x≤2
  2. x≥2
  3. x≤1
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x≤2 The result is x≤2.

Check 6

Solve −3x ≥ 6.

  1. x≤-2
  2. x≥-2
  3. x≤2
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x≤-2 The result is x≤-2.

Check 7

x is a whole number and 2x + 9 < 24. What is the largest possible value of x?

  1. 7
  2. 8
  3. 7.5
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7 The result is 7.

Check 8

How many whole numbers satisfy 4 ≤ x < 10?

  1. 6
  2. 7
  3. 8
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6 The result is 6.

Check 9

Solve 2x + 3 ≥ 13.

  1. x≥5
  2. x≤5
  3. x≥6.5
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x≥5 The result is x≥5.

Check 10

Solve 19 − 3x < 4.

  1. x>5
  2. x<5
  3. x>-5
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x>5 The result is x>5.

Check 11

x is a whole number and 2x + 5 < 14. What is the largest possible value of x?

  1. 4
  2. 5
  3. 4.5
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4 The result is 4.

Check 12

How many whole numbers satisfy −1 < x < 4?

  1. 4
  2. 5
  3. 6
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4 The result is 4.

Check 13

Solve 2x + 7 < 23.

  1. x<8
  2. x>8
  3. x<11.5
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x<8 The result is x<8.

Check 14

Solve −3x > 12.

  1. x<-4
  2. x>-4
  3. x<4
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x<-4 The result is x<-4.

Check 15

x is a whole number and 2x + 4 < 21. What is the largest possible value of x?

  1. 8
  2. 9
  3. 8.5
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8 The result is 8.

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