Solve the Equation: Determining X in 7.23 - 14x + 15.1x = 3.1x - 8.4

To solve this linear equation, follow these steps:

• Simplify both sides of the equation by combining like terms.
• Move all terms involving $x$ to one side of the equation.
• Isolate $x$ and solve for $x$.

Let's solve the equation step by step:

Step 1: Simplify both sides of the equation:
Combine the terms involving $x$:
$7.23 - 14x + 15.1x = 3.1x - 8.4$ simplifies to
$7.23 + (15.1x - 14x) = 3.1x - 8.4$.
This results in:
$7.23 + 1.1x = 3.1x - 8.4$.

Step 2: Move all terms involving $x$ to one side:
Subtract $1.1x$ from both sides to bring all $x$-terms to one side:
$7.23 = 3.1x - 1.1x - 8.4$.
Simplifies to:
$7.23 = 2x - 8.4$.

Step 3: Solve for $x$:
Add $8.4$ to both sides to isolate the constant term:
$7.23 + 8.4 = 2x$.
This gives us:
$15.63 = 2x$.
Now, divide both sides by 2 to solve for $x$:
$x = \frac{15.63}{2} = 7.815$.

Therefore, the solution to the equation is $x = 7.815$.