Question

solve the following compound inequality. -5 < (x - 4)/2 ≤ 1? < x ≤

Explanation:

Step1: Multiply all parts by 2

To eliminate the denominator, we multiply each part of the compound inequality by 2.
$$-5\times2 < \frac{x - 4}{2}\times2 \leq 1\times2$$
Simplifying each part gives:
$$-10 < x - 4 \leq 2$$

Step2: Add 4 to all parts

To solve for \(x\), we add 4 to each part of the inequality.
$$-10 + 4 < x - 4 + 4 \leq 2 + 4$$
Simplifying each part gives:
$$-6 < x \leq 6$$

Answer:

\(-6 < x \leq 6\)