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Linear inequalities in context
I can construct and solve linear inequalities from context.
Lesson 6 of 14
New
New
- Year 11
Linear inequalities in context
I can construct and solve linear inequalities from context.
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
Keywords
Inequality - An inequality is used to show that one expression may not be equal to another.
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?
Encourage pupils to discuss and share any examples of inequalities that they have come across in their lives. This helps them to see where their understanding of inequalities will be useful.
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
6 Questions
Q1.The solution to the inequality $$3a-8 \le 7$$ is when $$a \le$$ .
The solution to the inequality $$3a-8 \le 7$$ is when $$a \le$$ .
Correct Answer: 5
5
Q2.Which of these satisfies the inequality $$ 20 > 5(b-3) $$ ?
Which of these satisfies the inequality $$ 20 > 5(b-3) $$ ?
Correct answer: $$b=6$$
$$b=6$$
$$b=7$$
$$b=8$$
Correct answer: $$b=6.5$$
$$b=6.5$$
$$b=7.5$$
Q3.Which of these represents the inequality $$x<3$$ or $$x \ge 5$$ on a number line ?
Which of these represents the inequality $$x<3$$ or $$x \ge 5$$ on a number line ?
Correct Answer: An image in a quiz
Q4.Which of these is the solution to the inequality $$4 < 2x+2 < 10 $$ ?
Which of these is the solution to the inequality $$4 < 2x+2 < 10 $$ ?
Correct answer: $$1 < x < 4 $$
$$1 < x < 4 $$
$$1 < x < 10 $$
$$3 < x < 6 $$
$$3 < x < 10 $$
$$4 < x < 6 $$
Q5.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?
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?
$$2x$$
$$3x$$
$$4x$$
$$4x+4$$
Correct answer: $$6x$$
$$6x$$
Q6.Which of these is the solution to the inequality $$2x+5 < x+8 < 3x+4 $$ ?
Which of these is the solution to the inequality $$2x+5 < x+8 < 3x+4 $$ ?
$$-1 < x < 3 $$
$$-1 < x < 4 $$
Correct answer: $$2 < x < 3 $$
$$2 < x < 3 $$
$$2 < x < 4 $$
Assessment exit quiz
6 Questions
Q1.Match the inequalities to the written descriptions.
Match the inequalities to the written descriptions.
Correct Answer:$$x>15$$,Values more than 15
$$x>15$$ -Â Values more than 15
Correct Answer:$$x \ge 15$$,Values at least 15
$$x \ge 15$$ -Â Values at least 15
Correct Answer:$$x<15$$,Values under 15
$$x<15$$ -Â Values under 15
Correct Answer:$$x \le 15$$,Values which are 15 at most
$$x \le 15$$ -Â Values which are 15 at most
Q2.Which of these represents positive numbers less than 10?
Which of these represents positive numbers less than 10?
Correct answer: $$0 < x < 10$$
$$0 < x < 10$$
$$0 \le x < 10$$
$$0 < x \le 10$$
$$0 \le x \le 10$$
Q3.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?
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
Correct answer: $$1.2x \le 240$$ where $$x$$ is screen size in cm
$$1.2x \le 240$$ where $$x$$ is screen size in cm
Q4.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?
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 $$x \le 120$$
Correct answer: Any screen size $$x$$ cm when $$x \le 200$$
Any screen size $$x$$ cm when $$x \le 200$$
Any screen size $$x$$ cm when $$x \le 240$$
Any screen size $$x$$ cm when $$x \le 288$$
Q5.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?
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 $$x > 0$$
Correct answer: $$ 3(x+1) < 2x+5$$ and $$x > 0$$
$$ 3(x+1) < 2x+5$$ and $$x > 0$$
Q6.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?
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 $$-2.5 < x < 2$$
Correct answer: Any value $$x$$ where $$0 < x < 2$$
Any value $$x$$ where $$0 < x < 2$$
Any value $$x$$ where $$-2.5 < x < 4$$
Any value $$x$$ where $$0 < x < 4$$
