Question

The correct solution of \(-22 < 8x - 6 \leq 26\) is the interval:

• A. \((-2, 4]\)
• B. \([-2, 4]\)
• C. \((-2, 4)\)
• D. \([-2, 4)\)

Answer 1

The Correct Option is A

The given inequality is:
$-22 < 8x - 6 \le 26$.
Step 1: Break the inequality into two parts.
$-22 < 8x - 6$ and $8x - 6 \le 26$.
Step 2: Solve each part.
1. For $-22 < 8x - 6$:
$-22 + 6 < 8x \implies -16 < 8x \implies x > -2$.
2. For $8x - 6 \le 26$:
$8x \le 26 + 6 \implies 8x \le 32 \implies x \le 4$.
Step 3: Combine the two parts.
The combined inequality is:
$-2 < x \le 4$.
In interval notation:
$x \in (-2, 4]$.
Final Answer:
$(-2, 4]$