1. **Problem:** Calculate $5 + (-8)$. 2. **Formula:** Addition of integers, especially with negative numbers, follows the rule: adding a negative number is the same as subtracting its absolute value. 3. **Work:** $$5 + (-8) = 5 - 8 = -3$$ 4. **Explanation:** Starting at 5 on the number line, moving 8 units to the left lands at -3. 1. **Problem:** Calculate $-11 - 8$. 2. **Formula:** Subtracting a positive number moves left on the number line. 3. **Work:** $$-11 - 8 = -11 + (-8) = -19$$ 4. **Explanation:** From -11, move 8 units left to reach -19. 1. **Problem:** Calculate $-10 + 7$. 2. **Formula:** Adding a positive number moves right on the number line. 3. **Work:** $$-10 + 7 = -3$$ 4. **Explanation:** From -10, move 7 units right to reach -3. 1. **Problem:** Calculate $15 + (-6)$. 2. **Formula:** Adding a negative number is subtracting. 3. **Work:** $$15 + (-6) = 15 - 6 = 9$$ 4. **Explanation:** From 15, move 6 units left to reach 9. 1. **Problem:** Calculate $-9 - 10$. 2. **Formula:** Subtracting positive number moves left. 3. **Work:** $$-9 - 10 = -9 + (-10) = -19$$ 4. **Explanation:** From -9, move 10 units left to reach -19. **Note:** For the number line graph, plot each calculation starting point and move left or right according to the operation. **q_count**: 5