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 \(x \geqslant 2\) we can use the 'or' symbol.

\[\{ x: x < -6\} \cup \{x: x \geqslant 2\}\]