Solve the Equation for X: 7.1 + 3.18x - 1.14 = 9.14x + 3.5x + 1.9

To solve this linear equation, we'll follow these steps:

• Step 1: Combine like terms on each side of the equation.
• Step 2: Move all terms involving $x$ to one side of the equation.
• Step 3: Isolate the variable $x$ to solve for it.

Let's work through each step:

Step 1: Simplify both sides of the equation.
On the left side, combine like terms: $7.1 - 1.14 + 3.18x = 5.96 + 3.18x$.
On the right side, combine like terms involving $x$ and constant terms: $9.14x + 3.5x + 1.9 = 12.64x + 1.9$.

Step 2: Rearrange to move all $x$ terms to one side.
We start with the simplified equation: $5.96 + 3.18x = 12.64x + 1.9$.
Subtract $3.18x$ from both sides to get: $5.96 = 12.64x - 3.18x + 1.9$.

This simplifies to $5.96 = 9.46x + 1.9$.

Step 3: Isolate $x$ by performing arithmetic operations.
Subtract 1.9 from both sides: $5.96 - 1.9 = 9.46x$.
This gives us $4.06 = 9.46x$.

Finally, divide both sides by 9.46 to solve for $x$:
$x = \frac{4.06}{9.46} \approx 0.42$.

Therefore, the solution to the problem is $x = 0.42$.