Solve the Equation: 3.9 - 0.4X + 5.3X = 7.8 - 3.4 - 6.4X for the Value of X

To solve the given linear equation, we will follow these steps:

• Simplify each side of the equation by combining like terms.

• Rearrange terms to isolate all terms containing $x$ on one side and constants on the other.

• Solve for $x$ by simplifying the resulting equation.

Let's proceed with solving the equation:

Given equation: $3.9 - 0.4x + 5.3x = 7.8 - 3.4 - 6.4x$

Step 1: Simplify each side of the equation

On the left side, combine like terms:

$3.9 - 0.4x + 5.3x = 3.9 + 4.9x$

On the right side, simplify the constants:

$7.8 - 3.4 = 4.4$, thus $4.4 - 6.4x$

Step 2: Rearrange terms

Rearrange the equation to bring all $x$-terms to one side and constant terms to the other:

$3.9 + 4.9x = 4.4 - 6.4x$

Add $6.4x$ to both sides to move the $x$-terms to the left:

$3.9 + 4.9x + 6.4x = 4.4$

Simplify the equation:

$3.9 + 11.3x = 4.4$

Step 3: Solve for $x$

Subtract $3.9$ from both sides to isolate the terms with $x$:

$11.3x = 4.4 - 3.9$

$11.3x = 0.5$

Divide both sides by $11.3$ to solve for $x$:

$x = \frac{0.5}{11.3} \approx 0.044247787$

Rounded to two decimal places, $x$ is approximately:

$x = 0.04$

Therefore, the solution to the problem is $x = 0.04$.