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Lesson 7 of 14
  • Year 11
  • Higher

A single solution set

I can compare two solution sets from two different inequalities and define a solution set that satisfies both inequalities.

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View unit
Lesson 7 of 14
New
New
  • Year 11
  • Higher

A single solution set

I can compare two solution sets from two different inequalities and define a solution set that satisfies both inequalities.

Download all

Lesson details

Key learning points

  1. When combining solution sets, you may wish to use a number line
  2. Once you are certain, you can write the solution set using algebraic notation
  3. Both inequalities must be solved before the solution set can be determined

Keywords

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

Common misconception

Pupils may struggle to combine inequalities.

Encourage pupils to use a number line and draw on the potential solutions. In order for a solution set to be valid for all the stated inequalities, it must include values that satisfy all potential solution restrictions.


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

Pupils could use MWBs to draw their own number lines with mutliple inequalties shown on the number line. They could then have a peer try to work out how to express a single solution set.
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.
Which inequality represents all values which satisfy both of the drawn inequalities?

An image in a quiz
$$5 < x < 8$$
$$5 \le x \le 8$$
Correct answer: $$5 \le x < 8$$
$$5 < x \le 8$$

Q2.
Which inequality represents all values which satisfy both of the drawn inequalities?

An image in a quiz
$$x > 4$$
Correct answer: $$x \ge 6$$
$$4 < x \le 6$$
$$x < 4$$ or $$x \ge 6$$

Q3.
What inequality is represented on this number line?

An image in a quiz
$$4 < x < 5$$
$$4 < x \le 5$$
$$5 \le x < 4$$
$$x<4$$ or $$x > 5$$
Correct answer: $$x<4$$ or $$x \ge 5$$

Q4.
What is the solution to the inequality $$13>4x-7$$ ?

$$x < 1.5$$
$$x > 1.5$$
Correct answer: $$x < 5$$
$$x > 5$$

Q5.
Which of these shows all solutions to the inequality $$12 < 3(2x-4) < 24$$ ?

$$0 < x < 2$$
$$0 < x < 6$$
$$2 < x < 4$$
Correct answer: $$4 < x < 6$$

Q6.
Which of these shows all solutions to the inequality $$2x-6 < 3 - x < x+5$$ ?

$$-9 < x < 2$$
$$-9 < x < 9$$
$$-1 < x < 2$$
Correct answer: $$-1 < x < 3$$
$$5 < x < 9$$

Assessment exit quiz

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6 Questions

Q1.
What is the solution set for both inequalities represented on this number line simultaneously?

An image in a quiz
$$ 4 \le x < 5$$
$$ 4 \le x < 7$$
$$ 5 \le x < 7$$
Correct answer: $$5 < x < 7 $$

Q2.
What is the solution set for the inequalities $$ 5 < x < 10$$ and $$ x \le 8$$ simultaneously ?

Correct answer: $$5 < x \le 8$$
$$5 < x < 8$$
$$5 < x < 10$$
$$5 < x \le 10$$
$$8 \le x < 10$$

Q3.
What is the solution set for both these inequalities simultaneously: $$3x+4 < 10$$ and $$\frac{2x+3}{5}>-1$$?

$$-10 < x < -4$$
Correct answer: $$-4 < x < 2$$
$$-1 < x < 2$$
$$-1 < x < 10$$
$$2 < x < 10$$

Q4.
What is the solution set for both these inequalities simultaneously: $$5-2x < 7$$ and $$3(2x-5) \ge 3$$?

$$x > -1 $$
$$x < -1 $$
Correct answer: $$x \ge 3 $$
$$x \le 3 $$
$$-1 < x \le 3$$

Q5.
Which two inequalities have no solutions simultaneously?

$$11 < 2x+1 \le 17$$
Correct answer: $$3x-5 \le 13$$
$$ 4x > 16$$
Correct answer: $$\frac{x}{2} \ge 4$$

Q6.
Which two inequalities have exactly one solution simultaneously?

Correct answer: $$11 < 2x+1 \le 17$$
$$3x-5 \le 13$$
$$ 4x > 16$$
Correct answer: $$\frac{x}{2} \ge 4$$