1. **State the problem:** We need to solve the expression $-7 + 21$. 2. **Understand the operation:** This is an addition problem involving a negative and a positive number. 3. **Apply the rule:** When adding a negative number and a positive number, subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. 4. **Calculate the absolute values:** $|-7| = 7$ and $|21| = 21$. 5. **Subtract the smaller from the larger:** $21 - 7 = 14$. 6. **Determine the sign:** Since $21$ is positive and larger, the result is positive. 7. **Final answer:** $$-7 + 21 = 14$$