Answer:
To solve for y in the equation:
\[ \frac{7 + 8y}{15} - \frac{8}{3} = \frac{2y}{5} \]
You can follow these steps:
Step 1: Get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 15 in this case. This will clear the fractions.
\[ 15 \left( \frac{7 + 8y}{15} \right) - 15 \left( \frac{8}{3} \right) = 15 \left( \frac{2y}{5} \right) \]
This simplifies to:
\[ 7 + 8y - 40 = 6y \]
Step 2: Combine like terms on both sides of the equation.
\[ 8y - 6y = 40 - 7 \]
\[ 2y = 33 \]
Step 3: Finally, divide both sides by 2 to isolate y:
\[ \frac{2y}{2} = \frac{33}{2} \]
\[ y = \frac{33}{2} \]
So, the solution to the equation is:
\[ y = \frac{33}{2} \]