Linear Inequalities

We work with inequalities in a similar way to the way we work with equations, however there are a few key differences.

Solving Linear Inequalities

$$2x+3<7$$

Solve this in the same way as an equation.

$$2x<4$$

$$x<2$$

If we multiply and divide by a negative we must flip the inequality sign.

$$-2x>4$$

$$x<-2$$

Set Notation

A set is a group or collection of values.

We can write $x>6$ as:

$$\{x:x<6\}$$

This means 'the set of all values of x for which x is greater than 6'.

If a solution has $x<-6$ or $x⩾2$ we can use the 'or' symbol.

$$\{x:x<-6\}\cup \{x:x⩾2\}$$