Summary: Solving Equations Containing Decimals

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]