## Key Concepts

• Determine whether a number is a solution to an equation.
• Substitute the number for the variable in the equation.
• Simplify the expressions on both sides of the equation.
• Determine whether the resulting equation is true. If so, the number is a solution. If not, the number is not a solution.
• Properties of Equality
 Subtraction Property of Equality Addition Property of Equality For any numbers $a$ , $b$ , and $c$ , $\begin{array}{cccc}\text{If}& \hfill a& =& b\hfill \\ \text{then}& \hfill a-c& =& b-c\hfill \end{array}$ For any numbers $a$ , $b$ , and $c$ , $\begin{array}{cccc}\text{If}& \hfill a& =& b\hfill \\ \text{then}& \hfill a+c& =& b+c\hfill \end{array}$ Division of Property of Equality Multiplication Property of Equality For any numbers $a$ , $b$ , and $c\ne 0$ , $\begin{array}{cccc}\text{If}& \hfill a& =& b\hfill \\ \text{then}& \hfill \frac{a}{c}& =& \frac{b}{c}\hfill \end{array}$ For any numbers $a$ , $b$ , and $c$ , $\begin{array}{cccc}\text{If}& \hfill a& =& b\hfill \\ \text{then}& \hfill a\cdot c& =& b\cdot c\hfill \end{array}$