Question

solve the following compound inequality.
$-5 < \frac{x - 4}{2} \leq 1$
$? < x \leq $

Explanation:

Step1: Multiply all parts by 2

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

Step2: Add 4 to all parts

To isolate \( x \), we add 4 to each part of the inequality. So:
\( -10 + 4 < x - 4 + 4 \leq 2 + 4 \)
Simplifying each part, we have:
\( -6 < x \leq 6 \)

Answer:

\( -6 < x \leq 6 \) (So the first box is -6 and the second box is 6)