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The given compound inequality is:

\[
x < \frac{1}{2} \quad \text{and} \quad x > -\frac{1}{2}
\]

To solve this, we combine the two inequalities:

\[
-\frac{1}{2} < x < \frac{1}{2}
\]

This represents all values of \( x \) that lie between \(-\frac{1}{2}\) and \(\frac{1}{2}\), but not including \(\pm \frac{1}{2}\) themselves (because of the strict inequality).

In interval notation, the solution set is:

\[
\boxed{(-\frac{1}{2}, \frac{1}{2})}
\]

Thus, the correct choice is **A**, and the solution is:

\[
(-\frac{1}{2}, \frac{1}{2})
\]

Would you like further details on compound inequalities or any other related topic?

Here are 5 related questions to expand on this:

1. How do you solve compound inequalities with "or" instead of "and"?
2. What is the difference between strict inequalities and non-strict inequalities?
3. How do you represent inequalities on a number line?
4. How do you solve a compound inequality that involves absolute values?
5. What are some common mistakes to avoid when solving compound inequalities?

**Tip:** Always carefully observe whether inequalities are strict (<, >) or non-strict (≤, ≥), as this affects whether endpoints are included in the solution set.

Solve the compound inequality: \( \frac{1}{2} > x \) and \( x > -\frac{1}{2} \). What is the solution set?

Learn how to solve the compound inequality \( \frac{1}{2} > x \) and \( x > -\frac{1}{2} \) with a detailed step-by-step solution. This problem covers key algebraic concepts, including combining inequalities and expressing the solution in interval notation. Suitable for students in Grades 7-9.

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