1. The problem involves adding or subtracting negative numbers, which is called "Case 3" where you start with a negative number and make it more negative. 2. Rule #1 states: Adding a negative number is the same as subtracting a positive number. For example, $-2 + (-3)$ is the same as $-2 - 3$. 3. Let's solve the first problem: $-2 - 3$. 4. Using Rule #1, rewrite $-2 - 3$ as $-2 + (-3)$. 5. Now add the two negative numbers: $-2 + (-3) = -(2 + 3) = -5$. 6. This means starting at $-2$ on the number line and moving 3 units further left, ending at $-5$. 7. The final answer is $\boxed{-5}$. This same process applies to all the problems listed, where you add or subtract negative numbers by combining their absolute values and keeping the negative sign.