Inequalities using Set Notation

# Inequalities using Set Notation

GCSE(H),

Inequalities can be shown using set notation. The set notation is shown in the form:

{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.

To describe 4x + 5 > 25 in set notation, simplify to x > 5 and show as {x: > 5}. A description of the set notation is a set of numbers such that x > 5.

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

The inequalities can be shown in combinations, using set notation such as the union of two sets:

{x: < 4} uu {x: > 6}

## Examples

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

Answer: {x: > 2} nn {x: < -2}

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: > 2} nn {x: < -2}.

2. Which integers are described by this set description?

{x: > 4} nn {x: -3 ≤ x < 9}

Answer: 5, 6, 7, 8 and 9

The first set describes all integers that are 5 or greater. The seconds set describes integers from -3 to 9 inclusive. Integers in both sets are 5, 6, 7, 8 and 9.