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Determining Whether a Fraction is a Solution of an Equation

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

  1. Substitute the number for the variable in the equation.
  2. Simplify the expressions on both sides of the equation.
  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.

Example

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

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

Solution

  
 Determining Whether a Fraction is a Solution of an Equation
Determining Whether a Fraction is a Solution of an EquationDetermining Whether a Fraction is a Solution of an Equation
Change to fractions with a LCD of 10.Determining Whether a Fraction is a Solution of an Equation
Subtract.Determining Whether a Fraction is a Solution of an Equation

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

  
 Determining Whether a Fraction is a Solution of an Equation
Determining Whether a Fraction is a Solution of an EquationDetermining Whether a Fraction is a Solution of an Equation
 Determining Whether a Fraction is a Solution of an Equation
Subtract.Determining Whether a Fraction is a Solution of an Equation

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

  
 Determining Whether a Fraction is a Solution of an Equation
Determining Whether a Fraction is a Solution of an EquationDetermining Whether a Fraction is a Solution of an Equation
 Determining Whether a Fraction is a Solution of an Equation
Subtract.Determining Whether a Fraction is a Solution of an Equation

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

Optional Video: Solve One Step Equations With Fractions

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