Where can I download free solving inequalities PDF worksheets with answers?

On this MathsLinks page you can download free printable solving inequalities PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Corbett Practice, Corbett Textbook, Maths Made Easy, plus a printable one-page solving inequalities revision guide.

What GCSE grade is solving inequalities (4F)?

Solving inequalities (topic code 4F) is a Grade 4 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Solving inequalities Worksheets (PDF) with Answers — GCSE Maths

Free Solving inequalities PDF Worksheets & Answers

Grade 4 • Topic 4F

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
The Maths Room Online topic notes & examples	Page
Cognito Interactive online lesson & practice	Page

Grade 4 topics
4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction

Explanation:

Solve linear inequalities using the exact same inverse operations as linear equations, keeping the inequality sign (<, >, ≤, ≥) in the middle instead of an equals sign. Never replace the inequality sign with an = sign in your final answer!

Crucial rule: if you multiply or divide both sides by a negative number, you must flip the inequality sign around (or avoid negative x terms altogether by adding the negative x term to the other side).

Example 1: Solve 5x − 7 > 2x + 8

Solution:

Subtract 2x from both sides: 3x − 7 > 8

Add 7 to both sides: 3x > 15

Divide both sides by 3: x > 5

Answer: x > 5

Example 2: Solve the double inequality −5 ≤ 3x + 4 < 19 and state the largest integer x can be.

Solution:

Subtract 4 from all three parts: −9 ≤ 3x < 15

Divide all three parts by 3: −3 ≤ x < 5

Since x < 5, the largest integer is 4.

Answer: −3 ≤ x < 5; largest integer = 4

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Solving inequalities Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 IGCSE Jun 2019 2HR Q1 / 2FR Q17 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Write down the inequality shown on the number line. (1) (b) Solve 4y – 13 ≤ y + 8. (2)

(a) Write down the inequality shown on the number line. [1 mark]

(b) Solve the inequality 4y - 13 ≤ y + 8 [2 marks]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

x > –3

Answer (a): x > –3

Part (b) Solution:

3y ≤ 21 M1
⇒ y ≤ 7 A1

Answer (b): y ≤ 7

Past Paper Example 2 IGCSE Jun 2025 1HR Q6 / 1FR Q21 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Inequality shown on number line (2) (b) Solve 7a − 5 ≤ 3a + 28 (2)

(a) Write down the inequality shown on the number line. [2 marks]

(b) Solve the inequality 7a - 5 ≤ 3a + 28
Show clear algebraic working. [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

Solve like an equation using inverse operations. M1
e.g. 3m - 2 > 10 ⇒ 3m > 12 ⇒ m > 4
Answer: -2 < x ≤ 1 A1

Answer (a): -2 < x ≤ 1

Part (b) Solution:

4a ≤ 33 M1
⇒ a ≤ 8.25 A1

Answer (b): a ≤ 8.25

Past Paper Example 3 IGCSE Jun 2021 1F Q22 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Inequality on number line (b) Integer values of y for −4 ≤ 2y < 6 (c) Solve 7t − 3 ≤ 2t + 31

(a) Write down the inequality shown on the number line. [1 mark]

(b) Write down all the possible values of y. [2 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

x ≤ 2

Answer (a): x ≤ 2

Part (b) Solution:

−2 ≤ y < 3 M1
⇒ −2, −1, 0, 1, 2 A1

Answer (b): -2, -1, 0, 1, 2

Part (c) Solution:

5t ≤ 34 M1
⇒ t ≤ 6.8 A1

Answer (c): t ≤ 6.8

← 4E Inequalities on a number line

Back to GCSE questions by topic

4G Forming and solving equations →

Solving inequalities

Free Solving inequalities PDF Worksheets & Answers

Guide to Solving inequalities: Explanation, Diagrams & Worked Examples

GCSE Past Paper Solving inequalities Questions & Answers