Solve Linear Equation: 80-3.6x+7.4x=49+51-5.8x with Decimal Coefficients

To solve this linear equation, we will carefully combine like terms and isolate the variable $x$. Here are the steps:

• Step 1: Simplify both sides of the equation by combining like terms.
  On the left side: $80 - 3.6x + 7.4x = 80 + 3.8x$ (combining $-3.6x$ and $7.4x$).
• Step 2: Simplify the right side of the equation:
  $49 + 51 - 5.8x = 100 - 5.8x$. (Notice we combine $49$ and $51$ to get $100$).
• Step 3: Write the simplified equation:
  $80 + 3.8x = 100 - 5.8x$.
• Step 4: Move all $x$-terms to one side and constant terms to the other side by adding $5.8x$ to both sides and subtracting $80$ from both sides:
  $3.8x + 5.8x = 100 - 80$
• Step 5: Combine the $x$-terms and simplify constants:
  $9.6x = 20$.
• Step 6: Solve for $x$ by dividing both sides by $9.6$:
  $x = \frac{20}{9.6}$.
• Step 7: Compute the division:
  $x \approx 2.08$.

Upon looking at the choices provided, the correct choice is $\boxed{2.08}$, which is choice $2$.

Therefore, the solution to the problem is $x = 2.08$.