Linear inequalities in context | Maths | Quizalize & Oak National Academy

Starter quiz

The solution to the inequality $3a-8 \le 7$ is when $a \le$ ______.

'5' ✓
Which of these satisfies the inequality $20 > 5(b-3)$ ?

$b=6$ ✓

$b=7$

$b=8$

$b=6.5$ ✓

$b=7.5$
Which of these represents the inequality $x<3$ or $x \ge 5$ on a number line ?
Which of these is the solution to the inequality $4 < 2x+2 < 10$ ?

$1 < x < 4$ ✓

$1 < x < 10$

$3 < x < 6$

$3 < x < 10$

$4 < x < 6$
The length of a rectangle is double its width. If the width is $x$ which of these is an expression for the perimeter of the rectangle?

$2x$

$3x$

$4x$

$4x+4$

$6x$ ✓
Which of these is the solution to the inequality $2x+5 < x+8 < 3x+4$ ?

$-1 < x < 3$

$-1 < x < 4$

$2 < x < 3$ ✓

$2 < x < 4$

Exit quiz

Match the inequalities to the written descriptions.

$x>15$

⇔

Values more than 15 ✓

$x \ge 15$

⇔

Values at least 15 ✓

$x<15$

⇔

Values under 15 ✓

$x \le 15$

⇔

Values which are 15 at most ✓
Which of these represents positive numbers less than 10?

$0 < x < 10$ ✓

$0 \le x < 10$

$0 < x \le 10$

$0 \le x \le 10$
Izzy wants her sofa to be a distance from her TV which is exactly 1.2 times the screen size. She can put her sofa a maximum of 2.4 metres from her TV. Which inequality represents the TV she can get?

$x <240$ where $x$ is screen size in cm

$x \le 240$ where $x$ is screen size in cm

$1.2x <240$ where $x$ is screen size in cm

$1.2x \le 240$ where $x$ is screen size in cm ✓
Izzy wants her sofa to be a distance from her TV which is exactly 1.2 times the screen size. She can put her sofa a maximum of 2.4 metres from her TV. What size TV screen can she buy?

Any screen size $x$ cm when $x \le 120$

Any screen size $x$ cm when $x \le 200$ ✓

Any screen size $x$ cm when $x \le 240$

Any screen size $x$ cm when $x \le 288$
Sofia and Laura start with the same positive number. Sofia adds 1 then multiplies by 3. Laura multiplies by 2 then adds 5 and ends up with a larger number than Sofia. Which inequality represents this?

$0 < 2x+5 < 3(x+1)$

$0 < 3(x+1) < 2x+5$

$2x+5 < 3(x+1)$ and $x > 0$

$3(x+1) < 2x+5$ and $x > 0$ ✓
Sofia and Laura start with the same positive number. Sofia adds 1 then multiplies by 3. Laura multiplies by 2 then adds 5 and ends up with a larger number than Sofia. What could their start value be?

Any value $x$ where $-2.5 < x < 2$

Any value $x$ where $0 < x < 2$ ✓

Any value $x$ where $-2.5 < x < 4$

Any value $x$ where $0 < x < 4$

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Lesson Details

Key learning points

Inequalities are very common in real life
They are used when a constraint is needed
An example could be ensuring you do not exceed your budget for the week

Common misconception

Incorrectly interpreting inequalities due to the phrasing in English.

It can be helpful to think about the context when interpreting the phrasing. If a speed limit of 30 mph, would it be acceptable to do more than 30 mph? Is the car allowed to travel at a lower speed at any point?

Keywords

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