1. **State the problem:** We have three number cards with values $8$, $2$, and a missing number $x$. The median of these three numbers is $8$, and the range is $7$. 2. **Recall definitions:** - The median of three numbers is the middle value when they are arranged in order. - The range is the difference between the maximum and minimum values. 3. **Set up the median condition:** Since the median is $8$, when the three numbers $2$, $8$, and $x$ are sorted, $8$ must be the middle number. 4. **Analyze median condition:** For $8$ to be the median, $x$ must be either less than or equal to $8$ but greater than or equal to $2$, or greater than or equal to $8$ but less than or equal to some number. Since $2$ is the smallest, and $8$ is the median, $x$ must be greater than or equal to $8$ to keep $8$ in the middle. 5. **Set up the range condition:** The range is $7$, so $$\text{max} - \text{min} = 7$$ 6. **Identify min and max:** The minimum is $2$ (given), so $$\text{max} - 2 = 7 \implies \text{max} = 9$$ 7. **Determine $x$:** Since $x$ must be the maximum to satisfy the range, $$x = 9$$ 8. **Verify median:** The numbers are $2$, $8$, and $9$. Sorted: $2, 8, 9$. The median is indeed $8$. **Final answer:** The missing number is $9$.