## Determining Whether a Fraction is a Solution of an Equation

As we saw in Mathematics 102 and Mathematics 103, a solution of an equation is a value that makes a true statement when substituted for the variable in the equation. In those sections, we found whole number and integer solutions to equations. Now that we have worked with fractions, we are ready to find fraction solutions to equations.

The steps we take to determine whether a number is a solution to an equation are the same whether the solution is a whole number, an integer, or a fraction.

### Determining Whether a Fraction is a Solution of 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 it is true, the number is a solution. If it is not true, the number is not a solution.

## Example

Determine whether each of the following is a solution of \(x-\frac{3}{10}=\frac{1}{2}.\)

- \(x=1\)
- \(x=\frac{4}{5}\)
- \(x=-\frac{4}{5}\)

### Solution

Change to fractions with a LCD of 10. | |

Subtract. |

Since \(x=1\) does not result in a true equation, \(1\) is not a solution to the equation.

Subtract. |

Since \(x=\frac{4}{5}\) results in a true equation, \(\frac{4}{5}\) is a solution to the equation \(x-\frac{3}{10}=\frac{1}{2}.\)

Subtract. |

Since \(x=-\frac{4}{5}\) does not result in a true equation, \(-\frac{4}{5}\) is not a solution to the equation.