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.
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 it is true, the number is a solution. If it is not true, the number is not a solution.
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.
In other words, when you add or subtract the same quantity from both sides of an equation, or divide both sides by the same quantity, you still have equality.
Solve:
$y+\frac{9}{16}=\frac{5}{16}.$
Solution
Subtract
$\frac{9}{16}$ from each side to undo the addition.
Simplify on each side of the equation.
Simplify the fraction.
Check:
Substitute
$y=-\frac{1}{4}$ .
Rewrite as fractions with the LCD.
Add.
Since
$y=-\frac{1}{4}$ makes
$y+\frac{9}{16}=\frac{5}{16}$ a true statement, we know we have found the solution to this equation.
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