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