Answer
$x = 4$
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:
$\dfrac{4x}{6} - \dfrac{3}{6} = \dfrac{2x + 5}{6}$
Subtract the fractions:
$\dfrac{4x - 3}{6} = \dfrac{2x + 5}{6}$
Multiply each side of the equation by $6$ to eliminate the fractions:
$4x - 3 = 2x + 5$
Subtract $2x$ from each side of the equation:
$2x - 3 = 5$
Add $3$ to each side of the equation:
$2x = 8$
Divide each side of the equation by $2$:
$x = 4$
To check the solution, plug in $4$ for $x$ into the original equation:
$\dfrac{2(4)}{3} - \dfrac{1}{2} = \dfrac{2(4) + 5}{6}$
Simplify the fractions:
$\dfrac{8}{3} - \dfrac{1}{2} = \dfrac{13}{6}$
The LCD of these fractions is $6$. Convert fractions to equivalent fractions using the LCD:
$\dfrac{16}{6} - \dfrac{3}{6} = \dfrac{13}{6}$
Subtract to simplify:
$\dfrac{13}{6} = \dfrac{13}{6}$
Both sides are equal to one another; therefore, this solution is correct.
