To solve the equation \(8(1.3x + 0.25) - 6.7x = 3.8 + 2\), we can follow these steps:
Simplify the right side of the equation: \[ 3.8 + 2 = 5.8 \]
Distribute the \(8\) on the left side: \[ 8(1.3x) + 8(0.25) - 6.7x = 5.8 \] This simplifies to: \[ 10.4x + 2 - 6.7x = 5.8 \]
Combine like terms on the left side: \[ (10.4x - 6.7x) + 2 = 5.8 \] Which simplifies to: \[ 3.7x + 2 = 5.8 \]
Subtract \(2\) from both sides: \[ 3.7x = 5.8 - 2 \] This gives us: \[ 3.7x = 3.8 \]
Now, divide both sides by \(3.7\): \[ x = \frac{3.8}{3.7} \]
Calculate the result: \[ x \approx 1.027 \]
Thus, the solution is: \[ x \approx 1.027 \]