## Key Concepts

• How to determine whether a number is a solution to an equation.
• Step 1. Substitute the number for the variable in the equation.
• Step 2. Simplify the expressions on both sides of the equation.
• Step 3. Determine whether the resulting equation is true.
• If it is true, the number is a solution.
• If it is not true, the number is not a solution.
• Properties of Equalities
Subtraction Property of Equality Addition Property of Equality
For any numbers $a,b,c$,

if $a=b$ then $a-c=b-c$.

For any numbers $a,b,c$,

if $a=b$ then $a+c=b+c$.

• Division Property of Equality
• For any numbers $a,b,c$, and $c\ne 0$

If $a=b$ , then $\Large{\frac{a}{c}=\frac{b}{c}}$.