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Lesson 3 of 7
  • Year 11
  • Foundation

Inequalities on number lines

I can represent inequalities on a number line and what values satisfy an inequality based on the notation used.

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View unit
Lesson 3 of 7
New
New
  • Year 11
  • Foundation

Inequalities on number lines

I can represent inequalities on a number line and what values satisfy an inequality based on the notation used.

Download all

Lesson details

Key learning points

  1. Inequalities can be represented algebraically
  2. Inequalities can be represented graphically on a number line
  3. The diagram can indicate whether the inequality is a strict inequality
  4. Multiple inequalities can be shown on one number line

Keywords

  • Inequality - An inequality is used to show that one expression may not be equal to another.

Common misconception

Incorrectly interpreting the inequality diagram.

A filled in circle means the value is valid. An empty circle means the inequality is strict.


To help you plan your year 11 maths lesson on: Inequalities on number lines, download all teaching resources for free and adapt to suit your pupils' needs...

Pupils could use MWBs to draw their own inequalities on a number line and have a peer write the inequality represented. Additional challenge can be introduced by allowing multiple inequalities to be drawn on the same number line.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Match up the inequalities to the statements.

Correct Answer:$$x<-2$$,values less than -2

values less than -2

Correct Answer:$$x\le-2$$,values less than or equal to -2

values less than or equal to -2

Correct Answer:$$x>-2$$,values greater than -2

values greater than -2

Correct Answer:$$x\ge-2$$,values greater than or equal to -2

values greater than or equal to -2

Q2.
Which of these values satisfy the inequality $$x<3$$?

Correct answer: $$x=1$$
Correct answer: $$x=2$$
$$x=3$$
$$x=4$$
$$x=5$$

Q3.
Which of these values satisfy the inequality $$x\ge2$$?

$$x=-3$$
Correct answer: $$x=2$$
$$x=1.47$$
Correct answer: $$x=2.06$$
$$x=\frac{5}{6}$$

Q4.
Which of these values satisfy the inequality $$x>-1$$?

Correct answer: $$x=0$$
$$x=-1$$
$$x=-2$$
$$x=-\frac{4}{3}$$
Correct answer: $$x=-\frac{6}{7}$$

Q5.
Which of these values satisfy the inequality $$1<x\le3$$?

1
Correct answer: 3
5
Correct answer: 1.3
3.0004

Q6.
What is the value of $$a$$ on the number line?

An image in a quiz
Correct Answer: 18

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
Match the diagram to the correct inequality.

An image in a quiz
Correct Answer:A,$$x\le1$$

$$x\le1$$

Correct Answer:B,$$x\ge1$$

$$x\ge1$$

Correct Answer:C,$$x>1$$

$$x>1$$

Correct Answer:D,$$x<1$$

$$x<1$$

Q2.
What inequality is represented in this diagram?

An image in a quiz
$$-1<x<1$$
$$-1\le x \le 1$$
Correct answer: $$-1<x \le 1$$
$$-1\le x<1$$

Q3.
What inequality is represented in this diagram?

An image in a quiz
$$1<x<2$$
$$1\le x<2$$
$$1<x$$ or $$x>2$$
Correct answer: $$x\le 1$$ or $$x>2$$
$$x\le 1$$ or $$x\le 2$$

Q4.
Which diagram shows all values which satisfy both $$x<1$$ and $$x>0$$ ?

Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz

Q5.
Which inequality represents all values which satisfy both of the drawn inequalities?

An image in a quiz
$$1<x<2$$
$$x<1$$ or $$x>2$$
Correct answer: $$x<1$$
$$x<2$$

Q6.
Which inequality represents all values which satisfy both of the drawn inequalities?

An image in a quiz
$$-1\le x < 2$$
$$-1\le x < 1$$
Correct answer: $$0\le x < 1$$
$$0\le x < 2$$