Lesson 5: Equations

Property

Subtraction Property of Equality
For all real numbers $a$, $b$, and $c$, if $a = b$, then $a - c = b - c$.

Addition Property of Equality
For all real numbers $a$, $b$, and $c$, if $a = b$, then $a + c = b + c$.
When you add or subtract the same quantity from both sides of an equation, you still have equality.

Examples

• To solve $p - 7 = 12$, we use the Addition Property. Add 7 to both sides: $p - 7 + 7 = 12 + 7$, which simplifies to $p = 19$.

Property

Multiplication Property of Equality: For all real numbers $a$, $b$, $c$, if $a = b$, then $ac = bc$.

When you multiply both sides of an equation by the same quantity, you still have equality. This is used to 'undo' division in an equation.

Examples

• To solve $\frac{a}{-7} = -42$, we multiply both sides by $-7$. This results in $-7(\frac{a}{-7}) = -7(-42)$, which simplifies to $a = 294$.