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 three 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 \(-1 < x < 4\) as all values of \(x\) strictly between -1 and 4, not including -1 and 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 in the solution set.