1. **State the problem:** Solve the equation $7b - 15 = 5b - 3$ for $b$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing the same operations on both sides. 3. **Step 1:** Subtract $5b$ from both sides to get all $b$ terms on one side: $$7b - 5b - 15 = 5b - 5b - 3 \implies 2b - 15 = -3$$ 4. **Step 2:** Add $15$ to both sides to isolate the term with $b$: $$2b - 15 + 15 = -3 + 15 \implies 2b = 12$$ 5. **Step 3:** Divide both sides by $2$ to solve for $b$: $$b = \frac{12}{2} = 6$$ 6. **Answer:** The solution to the equation is $b = 6$. This means when $b$ is $6$, both sides of the original equation are equal.