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.
Is 3 a solution to this equation?
Substitute 3 for x
Since 29 is not equal to 24, 3 is not a solution to the equation.
Is the following inequality true or false?
$$x-4> 12,\, x=13$$
$$13> 16 \to false$$
$$y+5< 13,\, y=6$$
$$6< 8 \to true $$
Determine whether this inequality is true or false for y = 7