Solve the Linear Equation: Find X in 27.19 - 13.25X + 19.28 = 13.21X - 19.2X + 11.8

To solve the equation $27.19 - 13.25x + 19.28 = 13.21x - 19.2x + 11.8$, we will follow these steps:

• Simplify each side of the equation.
• Combine like terms to consolidate $x$ terms and constant terms separately.
• Isolate the variable $x$ on one side of the equation.

Let's start simplification:

1. Simplify the right side of the equation:
$13.21x - 19.2x = (13.21 - 19.2)x = -5.99x$,
so the right side becomes $-5.99x + 11.8$.

2. Simplify the left side of the equation:
Combine constants: $27.19 + 19.28 = 46.47$,
so the left side becomes $46.47 - 13.25x$.

Our equation now looks like:
$46.47 - 13.25x = -5.99x + 11.8$.

3. Combine like terms and solve for $x$:
Add $5.99x$ to both sides:
$46.47 - 13.25x + 5.99x = 11.8$,
Simplifying gives us $46.47 - 7.26x = 11.8$.

4. Isolate $x$ by subtracting 46.47 from both sides:
$-7.26x = 11.8 - 46.47$.
Simplifying gives $-7.26x = -34.67$.

5. Solve for $x$ by dividing by $-7.26$:
$x = \frac{-34.67}{-7.26} \approx 4.77$.

Therefore, the solution to the equation is $x = 4.77$, which matches the correct choice provided.