Inequalities can be shown using set notation:

{`x`: *inequality* }

where `x:` indicates the variable being described and *inequality* is written as an inequality, normally in its simplest form. The colon means *such that*.

For example: `{x: x > 5}`. This is read as `x` *such that* `x` *is greater than > 5*.

Sometimes the set is written with a bar instead of a colon: {`x¦ x > 5`}.

A more complex inequality would be shown as `{x: -5 < x < 5}`.

Write `x^2 - 4 > 0` in its simplest form in set notation.

Solve: `x^2 - 4 > 0` to get `x^2 > 4`

Square rooting gives two solutions: `x` must be greater than 2; or `x` must be less than -2: `{x: x > 2 or x < -2}`.

Answer: `{x: x > 2 or x < -2}`

Which integers are described by this set description?

`{x: x > 4} nn {x: -3 ≤ x < 9}`

The first set describes all integers that are 5 or greater. The second set describes integers from -3 to 8 (9 is not included). Integers in both sets are 5, 6, 7 and 8.

If necessary, check using a number line.

Answer: 5, 6, 7 and 8

See also Sets and Venn Diagrams

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