Solve Linear Equation: 7y + 10y + 5 = 2(y + 3)

To solve the equation $7y + 10y + 5 = 2(y + 3)$, let's proceed as follows:

• Step 1: Simplify the left side by combining like terms. The expression $7y + 10y$ combines to $17y$, so we have $17y + 5 = 2(y + 3)$.

• Step 2: Expand the right side. Distribute the 2 across the parenthesis: $2(y + 3)$ becomes $2y + 6$. The equation now reads $17y + 5 = 2y + 6$.

• Step 3: Isolate terms involving $y$ on one side. Subtract $2y$ from both sides: $17y - 2y + 5 = 6$, which simplifies to $15y + 5 = 6$.

• Step 4: Isolate $15y$ by subtracting 5 from both sides: $15y = 6 - 5$, which simplifies to $15y = 1$.

• Step 5: Solve for $y$ by dividing both sides by 15: $y = \frac{1}{15}$.

Therefore, the solution to the problem is $\mathbf{y = \frac{1}{15}}$.