To solve the equation \( 5(x + 2) = 2x + 19 \), we will start by distributing the \( 5 \) on the left side:
\[ 5(x + 2) = 5x + 10 \]
Now, we can rewrite the equation:
\[ 5x + 10 = 2x + 19 \]
Next, we want to isolate \( x \). We can do this by subtracting \( 2x \) from both sides:
\[ 5x - 2x + 10 = 19 \]
This simplifies to:
\[ 3x + 10 = 19 \]
Now, we'll subtract \( 10 \) from both sides to isolate the term with \( x \):
\[ 3x = 19 - 10 \]
This simplifies to:
\[ 3x = 9 \]
Finally, we divide both sides by \( 3 \) to solve for \( x \):
\[ x = \frac{9}{3} \]
Thus, we find:
\[ x = 3 \]
So, the solution to the equation is:
\[ \boxed{3} \]
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