Inequalities using Set Notation

## Inequalities using Set Notation

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}.

## Example 1

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}

## Example 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