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 [latex]a[/latex] , [latex]b[/latex] , and [latex]c[/latex] ,
[latex]\begin{array}{cccc}\text{If}& \hfill a& =& b\hfill \\ \text{then}& \hfill a-c& =& b-c\hfill \end{array}[/latex] |
For any numbers [latex]a[/latex] , [latex]b[/latex] , and [latex]c[/latex] ,
[latex]\begin{array}{cccc}\text{If}& \hfill a& =& b\hfill \\ \text{then}& \hfill a+c& =& b+c\hfill \end{array}[/latex] |
| Division of Property of Equality | Multiplication Property of Equality |
| For any numbers [latex]a[/latex] , [latex]b[/latex] , and [latex]c\ne 0[/latex] ,
[latex]\begin{array}{cccc}\text{If}& \hfill a& =& b\hfill \\ \text{then}& \hfill \frac{a}{c}& =& \frac{b}{c}\hfill \end{array}[/latex] |
For any numbers [latex]a[/latex] , [latex]b[/latex] , and [latex]c[/latex] ,
[latex]\begin{array}{cccc}\text{If}& \hfill a& =& b\hfill \\ \text{then}& \hfill a\cdot c& =& b\cdot c\hfill \end{array}[/latex] |
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