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      Solution set notation

      Lesson details

      Learning outcome

      I can represent a solution set using set notation.

      Key learning points

      1. A solution set can be presented in many different ways
      2. One of these ways is using set notation

      Keywords

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

      • Solution - A solution is a value, or set of values, that can be put in place of an unknown which makes the equation true.

      Common misconception

      3 > x > 9 is a valid way to combine x < 3 and x > 9

      Test a value to show pupils that this does not make sense. When x = 0, it is true that x < 3 but not true that x > 9 so 3 > 0 > 9 does not work.

      Teacher tip

      Have pupils draw their own number lines on MWBs and add inequalities to the number line. Have them swap with a partner and express the valid values using set notation.

      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.
      An inequality is used to show that one expression may __________ be equal to another.

      Correct answer: not
      actually
      well
      mathematically

      Q2.
      What inequality is represented on this number line?

      An image in a quiz
      $$x<2$$
      Correct answer: $$x>2$$
      $$x\le2$$
      $$x\ge2$$
      $$2<{x}<8$$

      Q3.
      Which integers satisfy this inequality? $$-2<{x}\le1$$

      $$-2$$
      Correct answer: $$-1$$
      Correct answer: $$0$$
      Correct answer: $$1$$
      $$0.1$$

      Q4.
      Which of these integer values satisfy both of these inequalities? $$-1<{x}$$ and $${x}\le3$$

      $$-2$$
      $$-1$$
      Correct answer: $$0$$
      Correct answer: $$3$$
      $$5$$

      Q5.
      Solve $$3(x-5)>9$$

      Correct answer: $$x>8$$
      $$x>5$$
      $$x<8$$
      $$x<5$$
      $$x>24$$

      Q6.
      Give any integer value which satisfies the inequality $$2x+8<5x-7\le38$$.

      Correct Answer: 6, 7, 8, 9

      6 Questions

      Q1.
      Rather than writing a pair of solutions as $$x<10$$ or $$x>15$$ we would write $${\{x: x<10}\}\cup{\{x: x>15}\}$$ This is called ...

      solution notation
      Correct answer: set notation
      inequality notation

      Q2.
      Which values satisfy these inequalities?

      An image in a quiz
      Correct answer: $${\{x: x\le-3}\}\cup{\{x: x>1}\}$$
      $${\{x: x\le-3}\}$$
      $${\{x: x>1}\}$$
      $$x>1$$
      $$x\le-3$$

      Q3.
      Which is the correctly written set notation for these inequalities?

      An image in a quiz
      $${\{-4<{x}\le-1}\}\cup{\{x>1}\}$$
      $${\{x: {x}\le-1}\}\cup{\{x: x>1}\}$$
      Correct answer: $${\{x: -4<{x}\le-1}\}\cup{\{x: x>1}\}$$
      $${\{x: -4<{x}\le-1}\}\cap{\{x: x>1}\}$$
      $${\{-4<{x}\le-1}\}{\{x>1}\}$$

      Q4.
      How many values are in this solution set? $${\{x:x \text { is an integer}}\}\cap{\{x:19<{x}\le27}\}$$

      Correct Answer: 8, Eight

      Q5.
      How many values are in this solution set? $${\{x:x \text { is an integer}}\}\cap{\{x:-3<{x}<1}\}$$

      None
      $$2$$
      Correct answer: $$3$$
      There are infinitely many

      Q6.
      Which of the below represents this set of values?

      An image in a quiz
      $${\{x:3\le{x}\le7}\}$$
      $${\{x:x \text { is an integer}}\}\cup{\{x:2<{x}<8}\}$$
      Correct answer: $${\{x:x \text { is an integer}}\}\cap{\{x:2<{x}<8}\}$$
      Correct answer: $${\{x:x \text { is an integer}}\}\cap{\{x:2<{x}\le7}\}$$
      $${\{x:x \text { is an integer}}\}\cap{\{x:2\le{x}\le7}\}$$

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