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

Advanced problem solving with linear inequalities

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

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

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

These inequalities model a company's packaging and production constraints. The values $$(15,20)$$ satisfy both inequalities __________.

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? {{}}

This model has three constraints. $$x$$ represents the number of standard games produced, $$y$$ the number of deluxe ones. What is the maximum number of games that can be made? {{}}

This model has three constraints. $$x =$$ standard games, making $$£4$$ profit. $$y =$$ deluxe games, making $$£9$$ profit. What is the maximum profit achievable? $$£$${{}}

$$5x+15y=1200$$ is an equation whereas $$5x+15y<1200$$ is an {{}}.

$$(5,2)$$ is the point of {{}} of these two linear equations.

A young person starts with $$£50$$ savings and then saves $$£15$$ per week. Which inequality represents the time when they will have more than $$£500$$ in savings?

Which of these values satisfy this inequality? $${8x+12y}\le{480}$$

Which of these values satisfy both of these inequalities simultaneously? $$y>2x+3$$ and $$y<12$$

Which of these values satisfy both of these inequalities simultaneously? $$y>2x+3$$ and $$y\le12-x$$

Advanced problem solving with linear inequalities

Lesson outcome