To solve the equation \( 0.8(10x + 13) = 3.1(0.2x + 5) \), we first expand both sides.
Starting with the left side:
\[ 0.8(10x + 13) = 0.8 \cdot 10x + 0.8 \cdot 13 = 8x + 10.4 \]
Now, for the right side:
\[ 3.1(0.2x + 5) = 3.1 \cdot 0.2x + 3.1 \cdot 5 = 0.62x + 15.5 \]
Now we can rewrite the equation with the expanded expressions:
\[ 8x + 10.4 = 0.62x + 15.5 \]
Next, we want to get all terms involving \(x\) on one side and constant terms on the other side. Subtract \(0.62x\) from both sides:
\[ 8x - 0.62x + 10.4 = 15.5 \]
This simplifies to:
\[ (8 - 0.62)x + 10.4 = 15.5 \]
Calculating \(8 - 0.62\):
\[ 7.38x + 10.4 = 15.5 \]
Next, subtract \(10.4\) from both sides:
\[ 7.38x = 15.5 - 10.4 \]
Calculating \(15.5 - 10.4\):
\[ 7.38x = 5.1 \]
Finally, we divide both sides by \(7.38\):
\[ x = \frac{5.1}{7.38} \]
Calculating \( \frac{5.1}{7.38} \):
\[ x \approx 0.691 \]
Thus, the final solution is:
\[ \boxed{0.691} \]