To solve the inequality \( 3(x + 4) \geq 2x + 5 \), we will first distribute the 3 on the left side:
\[ 3(x + 4) = 3x + 12 \]
Now, we can rewrite the inequality:
\[ 3x + 12 \geq 2x + 5 \]
Next, we will isolate \( x \) by subtracting \( 2x \) from both sides:
\[ 3x - 2x + 12 \geq 5 \]
This simplifies to:
\[ x + 12 \geq 5 \]
Now, we will subtract 12 from both sides:
\[ x \geq 5 - 12 \]
This simplifies to:
\[ x \geq -7 \]
The solution set for the inequality \( 3(x + 4) \geq 2x + 5 \) is:
\[ \boxed{[-7, \infty)} \]
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