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

A region is an area that graphically represents the solutions to one or more inequalities. Every coordinate pair within the region satisfies the inequalities that define the region.

Solving a set of linear inequalities graphically

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

This region satisfies both inequalities $$x>-5$$ and $$y<3$$...

Which region satisfies both inequalities simultaneously? $$y<-x$$ and $$x>-5$$

Which coordinate pairs satisfy both of these inequalities simultaneously? $$y<x$$ and $$y>2$$

In which region are all three of these inequalities satisfied simultaneously? $$y<4$$, $$y>x-3$$ and $$y>-x-2$$

In which region are all three of these inequalities satisfied simultaneously? $$y<4$$, $$y<x-3$$ and $$y>-x-2$$

No region can satisfy all three simultaneously

In which region are all three of these inequalities satisfied simultaneously? $$y>4$$, $$y<x-3$$ and $$y<-x-2$$

A region is an area that can graphically represent the solutions to one or more...

Which values satisfy this inequality? $$x\le-7$$

Which inequality is represented by this region?

Which of these coordinate pairs is in the region satisfied by $$y\geq-x$$?

Which of these coordinate pairs is in the region satisfied by $$y<4x+5$$?

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

Solving a set of linear inequalities graphically

Lesson outcome

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