5 - 6 y / 3 + y/8 = 0

To solve the equation \( 5 - \frac{6y}{3} + \frac{y}{8} = 0 \), we start by simplifying the expression.

1. Simplify \( \frac{6y}{3} \): \[ \frac{6y}{3} = 2y \] So the equation becomes: \[ 5 - 2y + \frac{y}{8} = 0 \]

2. Now, combine the \( -2y \) and \( \frac{y}{8} \). To do this, we'll express \( -2y \) with a common denominator of 8: \[ -2y = -\frac{16y}{8} \] Now rewrite the equation: \[ 5 - \frac{16y}{8} + \frac{y}{8} = 0 \] Combine the \( y \) terms: \[ 5 - \frac{16y - y}{8} = 0 \] Which simplifies to: \[ 5 - \frac{15y}{8} = 0 \]

3. Now isolate \( y \): \[ 5 = \frac{15y}{8} \]

4. Multiply both sides by 8 to eliminate the fraction: \[ 5 \cdot 8 = 15y \] \[ 40 = 15y \]

5. Divide by 15 to solve for \( y \): \[ y = \frac{40}{15} = \frac{8}{3} \]

So, the solution is: \[ y = \frac{8}{3} \]