Answer
$a = -1$
Work Step by Step
The least common denominator, or LCD, is $6$, in this case. Convert each fraction to an equivalent one that incorporates the LCD:
$\dfrac{2a + 1}{6} + \dfrac{3a}{6} = \dfrac{2a - 2}{6}$
Add the fractions:
$\dfrac{5a + 1}{6} = \dfrac{2a - 2}{6}$
Multiply each side of the equation by $6$ to eliminate the fractions:
$5a + 1 = 2a - 2$
Subtract $2a$ from each side of the equation:
$3a + 1 = -2$
Subtract $1$ from each side of the equation:
$3a = -3$
Divide each side of the equation by $3$:
$a = -1$
To check the solution, plug in $-1$ for $a$ into the original equation:
$\dfrac{2(-1) + 1}{6} + \dfrac{-1}{2} = \dfrac{-1 - 1}{3}$
Simplify the fractions:
$\dfrac{-1}{6} + \dfrac{-1}{2} = \dfrac{-2}{3}$
The LCD of all three fractions is $6$. Convert all fractions to equivalent ones that have $6$ as their denominator:
$-\dfrac{1}{6} - \dfrac{3}{6} = -\dfrac{4}{6}$
Combine like terms:
$-\dfrac{4}{6} = -\dfrac{4}{6}$
Both sides are equal to one another; therefore, this solution is correct.
