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Year 11
Higher

Solution set notation

I can represent a solution set using set notation.

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New
New
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.

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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: $${\{x:x \text { is an integer}}\}\cap{\{x:2<{x}\le7}\}$$
$${\{x:x \text { is an integer}}\}\cap{\{x:2\le{x}\le7}\}$$