Solve the following inequalities and express the answer in interval notation.

• A. $\left\lbrack4,10\right)$
• B. $\left(4,10\right\rbrack$
• C. $\left\lbrack0,6\right)$
• D. $\left(0,6\right\rbrack$

Answer: (B)

Verified step by step guidance

1. Start with the compound inequality given: \$1 < \frac{x - 2}{2} \le 4$.
2. To eliminate the fraction, multiply all parts of the inequality by 2 (which is positive, so the inequality signs remain the same): \$2 \times 1 < 2 \times \frac{x - 2}{2} \le 2 \times 4\(, simplifying to \)2 < x - 2 \le 8$.
3. Next, isolate \(x\) by adding 2 to all parts of the inequality: \$2 + 2 < x - 2 + 2 \le 8 + 2\(, which simplifies to \)4 < x \le 10$.
4. Interpret the inequality \$4 < x \le 10\( in interval notation. Since \)x\( is strictly greater than 4 but less than or equal to 10, the interval is \)(4, 10]$.
5. This interval represents all values of \(x\) that satisfy the original compound inequality.