Answer
$x = 2$
Work Step by Step
The least common denominator, or LCD, is $12$, in this case. Convert each fraction to an equivalent one that incorporates the LCD:
$\dfrac{3x - 2}{12} - \dfrac{2}{12} = \dfrac{2}{12}$
Subtract the fractions:
$\dfrac{3x - 4}{12} = \dfrac{2}{12}$
Multiply each side of the equation by $12$ to eliminate the fractions:
$3x - 4 = 2$
Add $4$ to each side of the equation:
$3x = 6$
Divide each side of the equation by $3$:
$x = 2$
To check the solution, plug in $2$ for $x$ into the original equation:
$\dfrac{3(2) - 2}{12} - \dfrac{1}{6} = \dfrac{1}{6}$
Simplify the fractions:
$\dfrac{4}{12} - \dfrac{1}{6} = \dfrac{1}{6}$
The LCD of these fractions is $12$. Convert fractions to equivalent fractions using the LCD:
$\dfrac{4}{12} - \dfrac{2}{12} = \dfrac{2}{12}$
Subtract to simplify:
$\dfrac{2}{12} = \dfrac{2}{12}$
Both sides are equal to one another; therefore, this solution is correct.
