A single solution set | Maths | Quizalize & Oak National Academy

Starter quiz

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

$5 < x < 8$

$5 \le x \le 8$

$5 \le x < 8$ ✓

$5 < x \le 8$
Which inequality represents all values which satisfy both of the drawn inequalities?

$x > 4$

$x \ge 6$ ✓

$4 < x \le 6$

$x < 4$ or $x \ge 6$
What inequality is represented on this number line?

$4 < x < 5$

$4 < x \le 5$

$5 \le x < 4$

$x<4$ or $x > 5$

$x<4$ or $x \ge 5$ ✓
What is the solution to the inequality $13>4x-7$ ?

$x < 1.5$

$x > 1.5$

$x < 5$ ✓

$x > 5$
Which of these shows all solutions to the inequality $12 < 3(2x-4) < 24$ ?

$0 < x < 2$

$0 < x < 6$

$2 < x < 4$

$4 < x < 6$ ✓
Which of these shows all solutions to the inequality $2x-6 < 3 - x < x+5$ ?

$-9 < x < 2$

$-9 < x < 9$

$-1 < x < 2$

$-1 < x < 3$ ✓

$5 < x < 9$

Exit quiz

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

$4 \le x < 5$

$4 \le x < 7$

$5 \le x < 7$

$5 < x < 7$ ✓
What is the solution set for the inequalities $5 < x < 10$ and $x \le 8$ simultaneously ?

$5 < x \le 8$ ✓

$5 < x < 8$

$5 < x < 10$

$5 < x \le 10$

$8 \le x < 10$
What is the solution set for both these inequalities simultaneously: $3x+4 < 10$ and $\frac{2x+3}{5}>-1$ ?

$-10 < x < -4$

$-4 < x < 2$ ✓

$-1 < x < 2$

$-1 < x < 10$

$2 < x < 10$
What is the solution set for both these inequalities simultaneously: $5-2x < 7$ and $3(2x-5) \ge 3$ ?

$x > -1$

$x < -1$

$x \ge 3$ ✓

$x \le 3$

$-1 < x \le 3$
Which two inequalities have no solutions simultaneously?

$11 < 2x+1 \le 17$

$3x-5 \le 13$ ✓

$4x > 16$

$\frac{x}{2} \ge 4$ ✓
Which two inequalities have exactly one solution simultaneously?

$11 < 2x+1 \le 17$ ✓

$3x-5 \le 13$

$4x > 16$

$\frac{x}{2} \ge 4$ ✓

Worksheet

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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

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.

Keywords

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