1. The problem is to solve the equation $$\frac{6b + 10}{4} = 7$$ for the variable $b$. 2. To solve for $b$, we first eliminate the denominator by multiplying both sides of the equation by 4: $$4 \times \frac{6b + 10}{4} = 7 \times 4$$ 3. This simplifies to: $$\cancel{4} \times \frac{6b + 10}{\cancel{4}} = 28$$ which reduces to: $$6b + 10 = 28$$ 4. Next, subtract 10 from both sides to isolate the term with $b$: $$6b + 10 - 10 = 28 - 10$$ which simplifies to: $$6b = 18$$ 5. Finally, divide both sides by 6 to solve for $b$: $$\frac{6b}{6} = \frac{18}{6}$$ $$\cancel{6}b / \cancel{6} = 3$$ which gives: $$b = 3$$ 6. Therefore, the solution is $b = 3$.