Solve the Linear Equation: 7.21 + 11.5x - 3.4x = 8.11x - 12.4 + 3.8

To solve this problem, let's carefully simplify and solve the given equation:

• Step 1: Simplify each side of the equation.
  Left side: $7.21 + 11.5x - 3.4x$ which simplifies to $7.21 + (11.5 - 3.4)x = 7.21 + 8.1x$.
  Right side: $8.11x - 12.4 + 3.8$ which simplifies to $8.11x - 8.6$.
• Step 2: Set up the simplified equation.
  We have $7.21 + 8.1x = 8.11x - 8.6$.
• Step 3: Move terms involving $x$ to one side and constants to the other.
  Subtract $8.1x$ from both sides: $7.21 = 8.11x - 8.6 - 8.1x$.
  This simplifies to $7.21 = 0.01x - 8.6$.
• Step 4: Solve for $x$.
  Add $8.6$ to both sides to isolate terms with $x$: $7.21 + 8.6 = 0.01x$, which simplifies to $15.81 = 0.01x$.
  Divide both sides by 0.01 to solve for $x$:
  $x = \frac{15.81}{0.01} = 1581$.

Therefore, the solution to the problem is $x = 1581$.