What is an inequality?

Definition

An inequality is a mathematical expression containing one or more unknowns, generally denoted by x. Unlike an equation (which uses the = sign), an inequality uses one of the following symbols:

Symbol	Meaning
<	strictly less than
>	strictly greater than
<=	less than or equal to
>=	greater than or equal to

A first-degree inequality with one unknown can always be written in the form a*x + b < c (or with >, <=, >=), where a, b and c are real numbers and a is not zero.

Practical example

The inequality 2x + 3 < 9 means: what are the values of x for which the number 2x + 3 is strictly less than 9?

Unlike an equation, which generally has a single solution, an inequality has an infinite number of solutions, which form an interval.

Checking a solution

To check whether x = 1 is a solution to 2x + 3 < 9, we substitute: 2 × 1 + 3 = 5, and 5 < 9 is true. Therefore, x = 1 is indeed a solution.

For x = 4: 2 × 4 + 3 = 11, and 11 < 9 is false. Therefore, x = 4 is not a solution.

Common pitfall

Do not confuse solving an equation (finding THE exact value) with solving an inequality (finding a WHOLE range of values). The answer to an inequality is never a single number, except in special cases.