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

• A. $[-6,8]$
• B. $[-\frac{3}{2},4]$
• C. $[-\frac{5}{2},3]$
• D. $[-10,6]$

Answer: (C)

Verified step by step guidance

1. Start with the compound inequality: \(-4 \le 2x + 1 \le 7\).
2. To isolate the term with \(x\), subtract 1 from all three parts of the inequality: \(-4 - 1 \le 2x + 1 - 1 \le 7 - 1\), which simplifies to \(-5 \le 2x \le 6\).
3. Next, divide all parts of the inequality by 2 to solve for \(x\): \(\frac{-5}{2} \le x \le 3\).
4. Express the solution in interval notation by writing the set of all \(x\) values between \(-\frac{5}{2}\) and \$3$, including the endpoints since the inequalities are inclusive.
5. The final answer is the interval \(\left[ -\frac{5}{2}, 3 \right]\).