1. **State the problem:** Solve the equation $\sin\left(\frac{1}{x}\right) = -2$. 2. **Recall the range of the sine function:** The sine function, $\sin(\theta)$, always has values between $-1$ and $1$ inclusive. That is, $-1 \leq \sin(\theta) \leq 1$ for all real $\theta$. 3. **Analyze the given equation:** The equation asks for $\sin\left(\frac{1}{x}\right) = -2$, but since $-2$ is outside the range of sine, there is no real value of $x$ that satisfies this. 4. **Conclusion:** There is no solution to the equation $\sin\left(\frac{1}{x}\right) = -2$ because the sine function cannot equal $-2$. **Final answer:** No solution exists.