Not Equal — Definition, Formula & Examples

Not equal means two values are different from each other. The symbol for not equal is ≠, which is an equals sign with a slash through it.

The relation $a \neq b$ states that the quantities $a$ and $b$ do not represent the same value. It is the logical negation of the equality relation $a = b$ .

Key Formula

a \neq b

Where:

$a$ = The value on the left side
$b$ = The value on the right side
$\neq$ = The not-equal symbol, meaning a and b are different values

How It Works

You use the not-equal symbol

\neq

whenever you want to show that two numbers, expressions, or variables have different values. For example, writing

3 \neq 5

tells the reader that 3 and 5 are not the same number. You can also use it with expressions:

2 + 1 \neq 5

because

2 + 1 = 3

, and 3 is not 5. In algebra,

x \neq 0

is often written to warn you that a variable cannot equal a certain value, such as when dividing by zero would be undefined.

Worked Example

Problem: Is the statement 4 + 3 ≠ 8 true or false?

Step 1: Evaluate the left side.

4 + 3 = 7

Step 2: Compare 7 to 8. Since 7 and 8 are different numbers, the not-equal statement is true.

7 \neq 8 \quad \text{is TRUE}

Answer: True. Since 7 is not the same as 8, the statement

4 + 3 \neq 8

is correct.

Why It Matters

You will see the

\neq

symbol throughout algebra, especially when stating restrictions on variables. For instance, in the expression

\frac{1}{x}

, you must write

x \neq 0

to avoid dividing by zero.

Common Mistakes

Mistake: Confusing ≠ with < or >.

Correction: The symbol ≠ only tells you two values are different — it does not tell you which one is larger. Use < or > when you need to show which value is greater.