Solve the Linear Equation: 8.51x + 3.4 - 6.14x = 7.51 + 3.8x - 6.1

To solve the linear equation $8.51x + 3.4 - 6.14x = 7.51 + 3.8x - 6.1$, we will proceed with these steps:

• Step 1: Combine like terms on the left side.
• Step 2: Combine like terms on the right side.
• Step 3: Isolate $x$ by collecting all $x$ terms on one side of the equation.
• Step 4: Solve for $x$.

Now, let's work through these steps in detail:

Step 1: Combining like terms on the left side:
The left side of the equation is $8.51x + 3.4 - 6.14x$.
Combine the $x$-terms: $(8.51 - 6.14)x + 3.4 = 2.37x + 3.4$.
The left side simplifies to $2.37x + 3.4$.

Step 2: Combining like terms on the right side:
The right side of the equation is $7.51 + 3.8x - 6.1$.
Combine the constant terms: $7.51 - 6.1 = 1.41$.
The right side simplifies to $3.8x + 1.41$.

Step 3: Isolate $x$:
Start with the equation $2.37x + 3.4 = 3.8x + 1.41$.
Subtract $2.37x$ from both sides to have $3.4 = (3.8 - 2.37)x + 1.41$.
This simplifies to $3.4 = 1.43x + 1.41$.

Subtract 1.41 from both sides to isolate the term with $x$:
$3.4 - 1.41 = 1.43x$, resulting in $1.99 = 1.43x$.

Step 4: Solve for $x$:
Divide both sides by $1.43$:
$x = \frac{1.99}{1.43} \approx 1.39$.

Therefore, the solution to the equation is $x = 1.39$.