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.

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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 resources

Share activities with pupils

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Lesson details

Key learning points

When combining solution sets, you may wish to use a number line
Once you are certain, you can write the solution set using algebraic notation
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.

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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

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

$$5 < x < 8$$

$$5 \le x \le 8$$

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

$$5 < x \le 8$$

Q2.

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

$$x > 4$$

Correct answer: $$x \ge 6$$

$$4 < x \le 6$$

$$x < 4$$ or $$x \ge 6$$

Q3.

What inequality is represented on this number line?

$$4 < x < 5$$

$$4 < x \le 5$$

$$5 \le x < 4$$

$$x<4$$ 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: $$-1 < x < 3$$

$$5 < x < 9$$

Exit quiz

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6 Questions

Q1.

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

$$ 4 \le x < 5$$

$$ 4 \le x < 7$$

$$ 5 \le x < 7$$

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: $$\frac{x}{2} \ge 4$$