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

A solution is a value, or set of values, that can be put in place of an unknown which makes the equation true.

Solution set notation

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

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

Rather than writing a pair of solutions as $$x<10$$ or $$x>15$$ we would write $${\{x: x<10}\}\cup{\{x: x>15}\}$$ This is called ...

Which is the correctly written set notation for these inequalities?

How many values are in this solution set? $${\{x:x \text { is an integer}}\}\cap{\{x:19<{x}\le27}\}$$ {{}}

How many values are in this solution set? $${\{x:x \text { is an integer}}\}\cap{\{x:-3<{x}<1}\}$$

$${\{x:x \text { is an integer}}\}\cup{\{x:2<{x}<8}\}$$

$${\{x:x \text { is an integer}}\}\cap{\{x:2<{x}<8}\}$$

$${\{x:x \text { is an integer}}\}\cap{\{x:2<{x}\le7}\}$$

$${\{x:x \text { is an integer}}\}\cap{\{x:2\le{x}\le7}\}$$

Which of the below represents this set of values?

An inequality is used to show that one expression may __________ be equal to another.

What inequality is represented on this number line?

Which integers satisfy this inequality? $$-2<{x}\le1$$

Which of these integer values satisfy both of these inequalities? $$-1<{x}$$ and $${x}\le3$$

Give any integer value which satisfies the inequality $$2x+8<5x-7\le38$$.

Solution set notation

Lesson outcome