Let's simplify the equation step by step:
Starting with the equation:
\[ 8(1.3x + 0.25) - 6.7x = 3.8 + 2 \]
Simplify the right side:
\[ 3.8 + 2 = 5.8 \]
Now the equation looks like:
\[ 8(1.3x + 0.25) - 6.7x = 5.8 \]
Distribute the 8 on the left side:
\[ 8 \cdot 1.3x + 8 \cdot 0.25 - 6.7x = 5.8 \]
\[ 10.4x + 2 - 6.7x = 5.8 \]
Combine like terms on the left side:
\[ (10.4x - 6.7x) + 2 = 5.8 \]
\[ 3.7x + 2 = 5.8 \]
Isolate the variable \(x\) by subtracting 2 from both sides:
\[ 3.7x = 5.8 - 2 \]
\[ 3.7x = 3.8 \]
Solve for \(x\) by dividing both sides by 3.7:
\[ x = \frac{3.8}{3.7} \]
\[ x \approx 1.027 \]
So the solution is:
\[ x \approx 1.027 \]