Solve the following inequalities and graph the solution.

• A.
• B.
• C.
• D.

Answer: (A)

Verified step by step guidance

1. Start with the compound inequality: \(-6 < 2x - 4 < 4\).
2. Add 4 to all three parts of the inequality to isolate the term with \(x\): \(-6 + 4 < 2x - 4 + 4 < 4 + 4\), which simplifies to \(-2 < 2x < 8\).
3. Divide all parts of the inequality by 2 to solve for \(x\): \(\frac{-2}{2} < \frac{2x}{2} < \frac{8}{2}\), which simplifies to \(-1 < x < 4\).
4. Interpret the solution: \(x\) is greater than \(-1\) and less than \(4\), so \(x\) lies between \(-1\) and \(4\) but does not include \(-1\) or \(4\) themselves.
5. Graph the solution on the number line by drawing an open interval (parentheses) from \(-1\) to \(4\), indicating that these endpoints are not included.