1. **State the problem:** Solve the inequality $$-13 \geq 2(b - 6) + 3$$ for $b$. 2. **Apply the distributive property:** $$-13 \geq 2b - 12 + 3$$ 3. **Simplify the right side:** $$-13 \geq 2b - 9$$ 4. **Isolate the term with $b$ by adding 9 to both sides:** $$-13 + 9 \geq 2b - 9 + 9$$ $$-4 \geq 2b$$ 5. **Divide both sides by 2 to solve for $b$:** $$\frac{-4}{\cancel{2}} \geq \frac{2b}{\cancel{2}}$$ $$-2 \geq b$$ 6. **Rewrite the inequality in a more standard form:** $$b \leq -2$$ **Final answer:** $$b \leq -2$$