\(\frac{3x + 1}{2} - \frac{4x + 3}{3} = 1\)
\(\frac{3(3x + 1)}{3(2)} - \frac{2(4x - 3)}{2(3)} = 1\)
\(\frac{3(3x) + 3(1)}{6} - \frac{2(4x) - 2(3)}{6} = 1\)
\(\frac{9x + 3}{6} - \frac{8x - 6}{6} = 1\)
\(\frac{(9x + 3) - (8x - 6)}{6} = 1\)
\(\frac{(9x - 8x) + (3 + 6)}{6} = 1\)
\(\frac{x + 9}{6} = 1\)
\(6(\frac{x + 9}{6}) = 1(6)\)
\(x + 9 = 6\)
\(x = -3\)
