#### Answer

x = 0

#### Work Step by Step

1. Given:
$\frac{4x + 1}{3} = \frac{x + 5}{6} + \frac{x - 3}{6}$
2. Multiply by LCD (6):
6($\frac{4x + 1}{3}) = (\frac{x + 5}{6} + \frac{x - 3}{6}$)6
3. Use distributive property to multiply:
2(4x + 1) = (x + 5) + (x - 3)
8x + 2 = 2x + 2
4. Add and subtract: 6x = 0
5. Divide: x = 0
6. Check: $\frac{4*0 + 1}{3} = \frac{0 + 5}{6} + \frac{0 - 3}{6}$
1/3 = 1/3, so 0 is a solution of the equation.