Answer
$x = \dfrac{2}{9}$
Work Step by Step
The least common denominator, or LCD, is $8$, in this case. Convert each fraction to an equivalent one that incorporates the LCD:
$\dfrac{2}{8} - \dfrac{8x}{8} = \dfrac{x}{8}$
Add the fractions:
$\dfrac{2 - 8x}{8} = \dfrac{x}{8}$
Multiply each side of the equation by $8$ to eliminate the fractions:
$-8x + 2 = x$
Subtract $x$ from each side of the equation:
$-9x + 2 = 0$
Subtract $2$ from each side of the equation:
$-9x = -2$
Divide each side of the equation by $-9$:
$x = \dfrac{2}{9}$
To check the solution, plug in $\frac{2}{9}$ for $x$ into the original equation:
$\dfrac{1}{4} - \dfrac{2}{9} = \dfrac{\frac{2}{9}}{8}$
Simplify the fractions:
$\dfrac{1}{4} - \dfrac{2}{9} = \dfrac{2}{72}$
The LCD of all three fractions is $72$. Convert all fractions to equivalent ones that have $72$ as their denominator:
$\dfrac{18}{72} - \dfrac{16}{72} = \dfrac{2}{72}$
Combine like terms:
$\dfrac{2}{72} = \dfrac{2}{72}$
Both sides are equal to one another; therefore, this solution is correct.
