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Year 11
Higher

Solution set notation

I can represent a solution set using set notation.

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New
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Year 11
Higher

Solution set notation

I can represent a solution set using set notation.

Download all resources
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Share activities with pupils
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Lesson details

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.


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

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.
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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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Starter quiz

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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

Exit quiz

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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: $${\{x:x \text { is an integer}}\}\cap{\{x:2<{x}\le7}\}$$
$${\{x:x \text { is an integer}}\}\cap{\{x:2\le{x}\le7}\}$$