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

To address the compound inequality \(-22<8x - 6 \leq 26\), we will separate it into two distinct inequalities and solve each one independently.

1. Inequality 1: \(-22<8x - 6\)

Add 6 to both sides:

\(-16<8x\)

Divide by 8:

\(-2<x\)

1. Inequality 2: \(8x - 6 \leq 26\)

Add 6 to both sides:

\(8x \leq 32\)

Divide by 8:

\(x \leq 4\)

Combining the results yields \(-2<x \leq 4\).

This corresponds to the interval \((-2, 4]\), which is the verified solution.