The problem asks us to solve the inequality $3(x + 1) \le 5(x + 2) + 15$.

1. Problem Description

The problem asks us to solve the inequality $3(x + 1) \le 5(x + 2) + 15$.

2. Solution Steps

We start by expanding the terms in the inequality:

$3(x + 1) \le 5(x + 2) + 15$

$3x + 3 \le 5x + 10 + 15$

$3x + 3 \le 5x + 25$

Now, we want to isolate $x$ on one side. Subtract $3x$ from both sides:

$3x + 3 - 3x \le 5x + 25 - 3x$

$3 \le 2x + 25$

Next, subtract 25 from both sides:

$3 - 25 \le 2x + 25 - 25$

$-22 \le 2x$

Now, divide both sides by 2:

$\frac{-22}{2} \le \frac{2x}{2}$

$-11 \le x$

This is equivalent to $x \ge -11$.

3. Final Answer

The solution to the inequality is $x \ge -11$.

The correct answer is D.