To solve the inequality \( 3(x + 4) \ge 2x + 5 \), we start by distributing the \( 3 \) on the left side:
\[ 3x + 12 \ge 2x + 5 \]
Next, we want to isolate \( x \) on one side of the inequality. We can do this by subtracting \( 2x \) from both sides:
\[ 3x - 2x + 12 \ge 5 \]
This simplifies to:
\[ x + 12 \ge 5 \]
Now, we subtract \( 12 \) from both sides:
\[ x \ge 5 - 12 \]
This simplifies to:
\[ x \ge -7 \]
Thus, the solution set for the inequality \( 3(x + 4) \ge 2x + 5 \) is:
\[ \boxed{[-7, \infty)} \]
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