To solve the equation \(\frac{2x + 1}{6} - \frac{3x - 1}{4} = 0\), we need to simplify the left-hand side and solve for x.
First, we need to find a common denominator for the two fractions. The smallest common multiple of 6 and 4 is 12, so we can rewrite the equation as:
\[\frac{2x+1}{6}\cdot \frac{2}{2} - \frac{3x-1}{4}\cdot \frac{3}{3} = 0\]
Simplifying, we get:
\[\frac{4x+2}{12} - \frac{9x-3}{12} = 0\]
Combining the fractions, we get:
\[\frac{4x+2-(9x-3)}{12} = 0\]
Simplifying further, we get:
\[\frac{-5x+5}{12} = 0\]
Multiplying both sides by 12, we get:
\[-5x+5=0\]
Adding 5 to both sides, we get:
\[-5x=-5\]
Dividing both sides by -5, we get:
\[x=1\]
Therefore, the solution to the equation is x = 1.