#### Answer

x = 0

#### Work Step by Step

1. Given:
$\frac{2x + 5}{5} = \frac{3x + 1}{2} + \frac{-x + 8}{16}$
2. Multiply by LCD (80):
80($\frac{2x + 5}{5}) = ( \frac{3x + 1}{2} + \frac{-x + 8}{16}$)80
3. Use distributive property to multiply:
16(2x + 5) = 40(3x + 1) + 5(-x + 8)
32x + 80 = 120x + 40 - 5x + 40
4. Add and subtract: -83x = 0
5. Divide: x = 0
6. Check: $\frac{2*0 + 5}{5} = \frac{3*0 + 1}{2} + \frac{-0 + 8}{16}$
1 = 1, so 0 is a solution of the equation.