Solve the following inequalities and express the answer in interval notation.
$-4\le 2x+1\le 7$

• A. $\(\left\[\lbrack\)-6,8\(\right\]\rbrack\)$
• B. $\(\left\[\lbrack\)-\(\frac\)32,4\(\right\]\rbrack\)$
• C. $\(\left\[\lbrack\)-\(\frac\)52,3\(\right\]\rbrack\)$
• D. $\(\left\[\lbrack\)-10,6\(\right\]\rbrack\)$

Answer: (C)

Verified step by step guidance

1. Start with the compound inequality: \(-4 \leq 2x + 1 \leq 7\).
2. Subtract 1 from all three parts of the inequality to isolate the term with \(x\): \(-4 - 1 \leq 2x + 1 - 1 \leq 7 - 1\), which simplifies to \(-5 \leq 2x \leq 6\).
3. Divide all parts of the inequality by 2 to solve for \(x\): \(\frac{-5}{2} \leq x \leq \frac{6}{2}\).
4. Simplify the fractions to get the solution in terms of \(x\): \(-\frac{5}{2} \leq x \leq 3\).
5. Express the solution in interval notation as \(\left[ -\frac{5}{2}, 3 \right]\), indicating that \(x\) includes both endpoints.