Lesson 1: Solving Two-Step 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

The Division Property of Equality: For any numbers $a$, $b$, and $c$, and $c \neq 0$, if $a = b$, then $\frac{a}{c} = \frac{b}{c}$.

The Multiplication Property of Equality: For any numbers $a$, $b$, and $c$, if $a = b$, then $ac = bc$.

Use these properties to isolate the variable by performing the inverse operation on both sides of the equation.