Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =.

$$x=y$$x is equal to y

Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

$$x>y$$x is greater than y

$$x≥y$$x is greater than or equal to y

$$x<y$$x is less than y

$$x≤y$$x is less than or equal to y

An equation or an inequality that contains at least one variable is called an open sentence.

When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.

**Example**

Is 3 a solution to this equation?

$$5x+14=24$$

Substitute 3 for x

$$5\cdot 3+14$$

$$5+14=29\neq 24$$

FALSE!

Since 29 is not equal to 24, 3 is not a solution to the equation.

**Example**

Is the following inequality true or false?

$$x-4> 12,\, x=13$$

$$13-4>12$$

$$13-4+4> 12+4$$

$$13> 16 \to false$$

$$y+5< 13,\, y=6$$

$$6+5<13$$

$$6+5-5< 13-5$$

$$6< 8 \to true $$

**Video lesson**

Determine whether this inequality is true or false for y = 7

$$y+8<24$$