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Inequalities on a number line Quiz

Grade 4 • 4E • 10 Questions (31 Marks)

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Inequalities on a number line — Notes & Worked Examples Show / Hide

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
Question 1
[2 marks]
Here is a number line.
–4–3–2–101234p
Write down the inequality shown on the number line.
Worked Solution & Answer
Filled circle at –3 means –3 ≤ p M1
open circle at 1 means p < 1 → –3 ≤ p < 1 A1
Answer: -3 ≤ p < 1
Question Paper (PDF) • Mark Scheme (PDF)
Question 2 OCR Jun 2025 1F Q16
[2 marks]
Write down the inequality shown on this number line.
x123456789
Worked Solution & Answer
Closed circle at 3 with arrow pointing to the right represents x ⩾ 3. M1 A1
Answer: x ≥ 3
Question Paper (PDF) • Mark Scheme (PDF)
Question 3
[3 marks]
(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 & Answer
(a)
Open circle at –1 pointing right ⇒ x > –1 B1
Answer (a): x > -1
(b)
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
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[3 marks]
(a) Number line shows y <= –2. Write down the largest possible integer value for y. (1)
(b) On a number line from –5 to 5, show the inequality –4 <= x < 2. (2)
(a) Write down the largest possible integer value for y. [1 mark]
y–5–4–3–2–1012345
(b) On the number line below, show the inequality -4 ≤ x < 2 [2 marks]
x–5–4–3–2–1012345
Worked Solution & Answer
(a)
The filled circle is at –2, so y ≤ –2. Largest integer = –2 B1
Answer (a): –2
(b)
Solid/closed circle at –4, hollow/open circle at 2, connected by a line M1 A1
x–5–4–3–2–1012345
Answer (b): Closed circle at –4, open circle at 2, line joining them
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 IGCSE Jan 2023 2HR Q3 / 2FR Q17
[3 marks]
-8 < 2y ≤ 2
y is an integer.
(a) Find all the possible values of y [2 marks]
(b) Write down the inequality shown on the number line. [1 mark]
x–5–4–3–2–1012345
Worked Solution & Answer
(a)
Divide by 2: -4 < y ≤ 1, so integer values are -3, -2, -1, 0, 1 M1 A1
Answer (a): -3, -2, -1, 0, 1
(b)
Open circle at -1 with arrow to the right represents x > -1 B1
Answer (b): x > -1
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 AQA Jun 2024 1H Q10
[3 marks]
(a) Represent –2 < x < 4 on the number line. [1 mark]
10 (b) Solve 5y + 14 ⩾ 11. [2 marks]
(a) Represent -2 < x < 4 on the number line. [1 mark]
x–5–4–3–2–1012345
(b) Solve 5y + 14 ≥ 11 [2 marks]
Answer
Worked Solution & Answer
(a)
Draw open circles above –2 and 4 and connect them B1
x–5–4–3–2–1012345
Answer (a): Open circles at –2 and 4 joined by a horizontal line
(b)
5y ⩾ 11 – 14 M1
⇒ 5y ⩾ –3
⇒ y ⩾ –3/5 (or –0.6) A1
Answer (b): Answer y ≥ -35 (or y ≥ -0.6)
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 AQA Jun 2024 1F Q26
[3 marks]
(a) Represent -2 < x < 4 on the number line.
26 (b) Solve 5y + 14 ≥ 11
(a) Represent -2 < x < 4 on the number line. [1 mark]
x–5–4–3–2–1012345
(b) Solve 5y + 14 ≥ 11 [2 marks]
Answer
Worked Solution & Answer
(a)
Draw open circles at -2 and 4, join with a solid horizontal line. B1
x–5–4–3–2–1012345
Answer (a): Open circle at -2, open circle at 4, line connecting them
(b)
5y ≥ 11 - 14 M1
5y ≥ -3
y ≥ -35 (or y ≥ -0.6) A1
Answer (b): Answer y ≥ -0.6
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 Specimen Set 2 3F Q20
[4 marks]
(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 & Answer
(a)
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
(b)
4y < 16 – 7 M1
⇒ 4y < 9
⇒ y < 9/4 (2.25) A1
Answer (b): y < 2.25
Question Paper (PDF) • Mark Scheme (PDF)
Question 9
[4 marks]
(a) Factorise fully 15w² – 5w (2)
(b) On the number line, show –2 < x ⩽ 4 (2)
(a) Factorise fully 15w2 - 5w [2 marks]
(b) On the number line below, show the set of values of x for which –2 < x ≤ 4 [2 marks]
–4–3–2–10123456
Worked Solution & Answer
(a)
Difference of two squares: a2 - b2 = (a + b)(a - b) M1
e.g. m2 - 9 = (m + 3)(m - 3)
Answer: 5w(3w - 1) A1
Answer (a): 5w(3w - 1)
(b)
Open circle at –2, closed circle at 4, joined by a line M1 A1
–4–3–2–10123456
Answer (b): Open circle at –2, closed circle at 4, joined by a line
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[4 marks]
Jenna is asked to show the inequality -3 < x ≤ 4 on a number line.
Here is her answer.
x–5–4–3–2–1012345
(a) Write down two mistakes Jenna has made. [2 marks]
(b) Work out the greatest integer that satisfies the inequality
5y - 7 < 16 [2 marks]
Worked Solution & Answer
(a)
1. The circle at –2 should be at –3. 2. The circle at 4 should be shaded/filled in. M1 C1
Answer (a): 1. The circle at –2 should be at –3. 2. The circle at 4 should be shaded/filled in.
(b)
5y < 23 M1
⇒ y < 4.6
⇒ greatest integer is 4 A1
Answer (b): 4
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 31 marks)
Inequalities on a number line Worksheets Next: Solving inequalities →

Grade 4 Quizzes

24 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