Solve the compound inequality. Express the answer in interval notation.
(B) $x+1\le 9$ and $x+2>3$

• A. $(1,2]$
• B. $(5,10]$
• C. $(3,9]$
• D. $(1,8]$

Answer: (D)

Verified step by step guidance

1. Start by writing down the compound inequality: \(x + 1 \leq 9\) and \(x + 2 > 3\).
2. Solve the first inequality \(x + 1 \leq 9\) by subtracting 1 from both sides to isolate \(x\): \(x \leq 9 - 1\).
3. Simplify the right side to get \(x \leq 8\).
4. Solve the second inequality \(x + 2 > 3\) by subtracting 2 from both sides: \(x > 3 - 2\).
5. Simplify the right side to get \(x > 1\). Now combine both inequalities to write the solution as \$1 < x \leq 8\(, which in interval notation is \)(1, 8]$.