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 $\Large{\frac{a}{c}=\frac{b}{c}}$.