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

Linear inequalities in context

Maths

Checking and securing understanding of simultaneous equations

Non-solutions to simultaneous linear equations

Inequalities on number lines

Solving simple linear inequalities

Solving more complicated linear inequalities

A single solution set

Solution set notation

Solving a linear inequality graphically

Solving a set of linear inequalities graphically

Relating graphical solutions to algebraic solutions for inequalities

Solving quadratic inequalities in one variable graphically

Solving quadratic inequalities algebraically

Advanced problem solving with linear inequalities

In this unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

In this unit, pupils extend their understanding of inequalities and consider a range of contextual inequalities and ways to find and represent their solutions.

Inequalities

Match the inequalities to the written descriptions.

Which of these represents positive numbers less than 10?

$$x <240$$ 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. Which inequality represents the TV she can get?

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 $$x \le 288$$

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?

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. What could their start value be?

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

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

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 $$4 < 2x+2 < 10 $$ ?

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?

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

Starter Quiz

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