# Inequalities

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

$$y+8<24$$