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

• A. $\left(1,2\right\rbrack$
• B. $\left(5,10\right\rbrack$
• C. $\left(3,9\right\rbrack$
• D. $\left(1,8\right\rbrack$

Answer: (D)

Verified step by step guidance

1. Start by writing down the two inequalities separately: \(x + 1 \leq 9\) and \(x + 2 > 3\).
2. Solve the first inequality for \(x\) by subtracting 1 from both sides: \(x \leq 9 - 1\) which simplifies to \(x \leq 8\).
3. Solve the second inequality for \(x\) by subtracting 2 from both sides: \(x > 3 - 2\) which simplifies to \(x > 1\).
4. Since this is a compound inequality connected by 'and', find the intersection of the two solution sets: \(x > 1\) and \(x \leq 8\).
5. Express the solution in interval notation by combining the inequalities into one interval: \((1, 8]\).