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

A single solution set

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

Linear inequalities in context

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

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

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

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

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

Which two inequalities have no solutions simultaneously? 

Which two inequalities have exactly one solution simultaneously? 

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

What inequality is represented on this number line?

What is the solution to the inequality $$13>4x-7$$ ?

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

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

A single solution set

Lesson outcome