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

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

A single solution set

Solution set notation

Solving a linear inequality 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

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 $$y<4x+5$$?

Solving a set of linear inequalities graphically

Lesson outcome