1. **State the problem:** Solve the inequality $$5 + 2(6b - 10) > -b + 8 - 7$$ for $b$ and write the answer in simplest form. 2. **Expand and simplify both sides:** $$5 + 2(6b - 10) > -b + 8 - 7$$ $$5 + 12b - 20 > -b + 1$$ 3. **Combine like terms on the left side:** $$12b - 15 > -b + 1$$ 4. **Add $b$ to both sides to get all $b$ terms on one side:** $$12b + b - 15 > 1$$ $$13b - 15 > 1$$ 5. **Add 15 to both sides to isolate the term with $b$:** $$13b - 15 + 15 > 1 + 15$$ $$13b > 16$$ 6. **Divide both sides by 13 to solve for $b$:** $$\frac{\cancel{13}b}{\cancel{13}} > \frac{16}{13}$$ $$b > \frac{16}{13}$$ **Final answer:** $$b > \frac{16}{13}$$