Solve the Linear Equation: 5.1x - 4 = 3.8x + 5 - 1.2x

To solve the equation $3.8 + 5.1x - 4 = 3.8x + 5 - 1.2x$, we will follow these steps:

• Step 1: Simplify both sides of the equation by combining like terms.
• Step 2: Isolate the terms containing $x$ on one side and the constants on the other.
• Step 3: Solve for $x$.

Let's proceed step-by-step:

Step 1: Simplify both sides of the equation.
Left Side: $3.8 + 5.1x - 4$ simplifies to $5.1x - 0.2$.
Right Side: $3.8x + 5 - 1.2x$ simplifies to $2.6x + 5$.

The equation now is:

$5.1x - 0.2 = 2.6x + 5$

Step 2: Isolate the variable term:
Subtract $2.6x$ from both sides to get:

$5.1x - 2.6x - 0.2 = 5$

Which simplifies to:

$2.5x - 0.2 = 5$

Add $0.2$ to both sides to get:

$2.5x = 5.2$

Step 3: Solve for $x$ by dividing both sides by $2.5$:

$x = \frac{5.2}{2.5}$

Calculating the division, we obtain:

$x = 2.08$

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