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Inequalities on a number line

Free Printable Inequalities on a number line PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 4)

Download free inequalities on a number line worksheets (PDF), GCSE maths past paper questions and worked solutions for Inequalities on a number line (4E). This is a Grade 4 algebra topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Made Easy, Dr Frost, Dr Austin, 1st Class Maths, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our inequalities on a number line revision notes and worked examples with diagrams, try real GCSE past paper inequalities on a number line questions with step-by-step solutions, or download a PDF of all inequalities on a number line worksheet links.

Free Inequalities on a number line PDF Worksheets & Answers

Grade 4 • Topic 4E
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Grade 4 topics
4A - Compound interest4B - Indices (index laws)
4C - Prime factors HCF and LCM4D - Real life graphs
4E - Inequalities on a number line4F - Solving inequalities
4G - Forming and solving equations4H - nth term of a linear sequence
4J - Expanding and factorising4K - Pythagoras theorem
4L - Angles in parallel lines4M - Angles in polygons
4N - Surface area4P - Volume of a cuboid
4Q - Volume of a prism4R - Bearings
4S - Cylinders4T - Plans and elevations
4U - Scatter graphs4V - Probability
4W - Averages from tables4X - Reverse mean
4Y - Area of a trapezium4Z - Loci and construction
GCSE Maths Grade 4 Revision Notes & Method

Guide to Inequalities on a number line: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

On a number line, an open (unshaded) circle ○ is used for strict inequalities (< or >, where the endpoint is not included), and a closed (filled) circle ● is used for inclusive inequalities (≤ or ≥, where the endpoint is included).

A single inequality has an arrow pointing left (< or ≤) or right (> or ≥). A double inequality like −2 < x ≤ 3 is drawn as a line segment joining two circles at −2 and 3. Remember that integers are whole numbers (positive, negative, or zero).

Example 1: Represent −2 < x ≤ 3 on a number line and list all integers that satisfy it.

-3 -2 -1 0 1 2 3
Open circle at −2 (<), closed circle at 3 (≤).
Integers: −1, 0, 1, 2, 3

Example 2: Write down the inequality shown on the number line below.

-3 -2 -1 0 1 2 3 4 5
Filled at −1 (left) → x ≤ −1;  open at 4 (right) → x > 4
Answer: x ≤ −1  or  x > 4
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Inequalities on a number line Questions & Answers

Past Paper Example 1 GCSE Nov 2021 2F Q21 / 2H Q1 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Write down the inequality shown on the number line. (1) (b) Show –3 ⩽ y < 4 on the number line. (2)
(a) Write down the inequality shown on this number line. [1 mark]
x–5–4–3–2–1012345
(b) On the number line below, show the inequality -3 ≤ y < 4 [2 marks]
y–5–4–3–2–1012345
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
Open circle at –1 pointing right ⇒ x > –1 B1
Answer (a): x > -1
Part (b) Solution:
Filled circle at –3, hollow circle at 4, connected M1 A1
y–5–4–3–2–1012345
Answer (b): Closed circle at –3, open circle at 4, joined by a line
Past Paper Example 2 GCSE Nov 2019 1F Q19 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Here is a number line.
–4–3–2–101234p
Write down the inequality shown on the number line.
Worked Solution & Mark Scheme (2 marks)
Filled circle at –3 means –3 ≤ p M1
open circle at 1 means p < 1 → –3 ≤ p < 1 A1
Answer: -3 ≤ p < 1
Past Paper Example 3 Specimen Set 2 3F Q20 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Show the inequality –2 ⩽ x < 3 on the number line. (2) (b) Solve the inequality 4y + 7 < 16 (2)
(a) Show the inequality -2 ≤ x < 3 on the number line below. [2 marks]
x–4–3–2–1012345
(b) Solve the inequality 4y + 7 < 16 [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Filled circle at –2, open circle at 3, line joining them M1 A1
x–4–3–2–1012345
Answer (a): Filled circle at –2, open circle at 3, line joining them
Part (b) Solution:
4y < 16 – 7 M1
⇒ 4y < 9
⇒ y < 9/4 (2.25) A1
Answer (b): y < 2.25

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