1. The problem is to determine the relationship between the fractions $\frac{-1}{2}$ and $\frac{2}{3}$ in the context of set inclusion, denoted by $\subseteq$. 2. Set inclusion $A \subseteq B$ means every element of set $A$ is also an element of set $B$. Here, the notation $\frac{-1}{2} \subseteq X \frac{2}{3}$ is ambiguous because individual fractions are not sets by themselves. 3. If the problem means to compare the values of the fractions, we evaluate: $$\frac{-1}{2} = -0.5,\quad \frac{2}{3} \approx 0.6667$$ 4. Since $-0.5$ is less than $0.6667$, we can conclude $\frac{-1}{2} < \frac{2}{3}$ but not that one is a subset of the other, as they are single numbers, not sets. 5. If this problem involves intervals or sets generated by these fractions (e.g., intervals on the number line), please clarify the definition of the sets $X$ or additional context. Final answer: $\frac{-1}{2}$ and $\frac{2}{3}$ are numbers, so $\frac{-1}{2} \subseteq X \frac{2}{3}$ is not a valid statement without more context.