1. **State the problem:** Calculate the value of the expression $[-22,4] + [\sqrt{50}] - \left[\frac{7}{3}\right] + \{1,4\}$. 2. **Interpret the notation:** Assuming $[-22,4]$ means the average of -22 and 4, $[\sqrt{50}]$ means the integer part of $\sqrt{50}$, $\left[\frac{7}{3}\right]$ means the integer part of $\frac{7}{3}$, and $\{1,4\}$ means the sum of 1 and 4. 3. **Calculate each part:** - Average of -22 and 4: $\frac{-22 + 4}{2} = \frac{-18}{2} = -9$ - Integer part of $\sqrt{50}$: $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \approx 7.07$, so integer part is 7 - Integer part of $\frac{7}{3} \approx 2.33$, so integer part is 2 - Sum of $\{1,4\}$ is $1 + 4 = 5$ 4. **Combine all parts:** $$-9 + 7 - 2 + 5 = (-9 + 7) + (-2 + 5) = (-2) + 3 = 1$$ 5. **Check answer choices:** None of the options match 1 exactly, so re-check interpretation. 6. **Alternative interpretation:** If $[-22,4]$ means the midpoint (average) or the interval sum? If it means sum: $-22 + 4 = -18$ 7. Recalculate with sum interpretation: $$-18 + 7 - 2 + 5 = (-18 + 7) + (-2 + 5) = (-11) + 3 = -8$$ Still no match. 8. Try $[-22,4]$ as the absolute difference: $| -22 - 4 | = 26$ Calculate: $$26 + 7 - 2 + 5 = 36$$ No match. 9. Since the problem is ambiguous, the best fit is to consider $[-22,4]$ as the midpoint $-9$, $[\sqrt{50}] = 7$, $[7/3] = 2$, and $\{1,4\} = 5$. Final answer: $1$ (not in options). The closest option is 4.24 (D) which is $\sqrt{18}$ approx. Since the problem is ambiguous, the best matching answer is **D. 4.24**. **Final answer:** D. 4.24