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

Problem solving with linear inequalities

Maths

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.

Inequalities

The graph shows the charges of three taxi firms. The coordinate pair $$(3,9)$$ is the point of __________ of the graphs of taxi firms 'a' and 'b'.

In what region does taxi firm 'a' charge less than taxi firm 'b'?

In what region does taxi firm 'c' charge less than taxi firm 'a'?

These inequalities model a company's packaging and production constraints. Which of these points satisfies the production constraint but not the packaging constraint?

These inequalities model a company's packaging and production constraints. Which of these points satisfy both the production and the packaging constraints?

These inequalities model a company's packaging and production constraints. Which coordinate pair is the point where both production and packaging are optimised? {{}}

$$15x+25y=1500$$ is an equation whereas $$15x+25y<1500$$ is an {{}}.

Which of these is the point of intersection of these two linear equations?

For the equation $$c=10+6m$$ what is the value of $$c$$ when $$m=9$$? $$c=$${{}}.

Which of these values satisfy this inequality? $${3x+6y}\le{450}$$

A taxi firm charge a fixed rate of $$£4$$ per journey plus $$£1.50$$ per mile travelled. The cost of your journey cannot exceed $$£16$$. Which inequality models this scenario?

This lesson will be removed by end of Summer Term 2025.

Problem solving with linear inequalities

Lesson outcome

This lesson will be removed by end of Summer Term 2025.