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      Inequalities on number lines

      Lesson details

      Learning outcome

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

      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.

      Teacher tip

      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.

      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

      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

      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: $$0\le x < 1$$
      $$0\le x < 2$$

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