1. The problem is to find the value of $-7 + 11$. 2. We use the rule of addition for integers: adding a positive number to a negative number involves subtracting the smaller absolute value from the larger absolute value and taking the sign of the number with the larger absolute value. 3. Calculate the absolute values: $|-7| = 7$ and $|11| = 11$. 4. Since $11 > 7$, subtract $7$ from $11$: $$11 - 7 = 4$$ 5. The sign of the result is positive because $11$ is positive. 6. Therefore, $$-7 + 11 = 4$$ 7. The final answer is 4.