Inequalities

In an equation the '\({=}\)' sign means the two sides are identical. But what happens when the two sides are not identical?

If this is the case you need to use inequalities to show the relationship between the two sides.

  • \(\textless\) means 'less than'
  • \(\leq\) means 'less than or equal to'
  • \(\textgreater\) means 'greater than'
  • \(\geq\) means 'greater than or equal to'

For example, if \(x \textgreater 2\), then \(x = 3,~4,~5,~6,~7,~...\) (\(x\) is greater than, but not equal to \(2\), so don't include the \(2\)).

If \(y\) is \(\leq 4\), then \(y = 4,~3,~2,~1,~0,~-1,~...\) (\(y\) is less than or equal to \(4\), so do include the \(4\)).

Question

If \(z \geq 3\), what are the possible values of \(z\)?

\[3,~4,~5,~6,~7,~8,~...\]

\(z\) is greater than or equal to \(3\), so it can be \(3\) or any number greater than \(3\).