Solving the Equation: 0.3x + 7.4x = 3.8x - 3.5 + 1.4

To solve the equation $0.3x - 4.5 + 7.4x = 3.8x - 3.5 + 1.4$, we will follow these steps:

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

Let's work through each step:

Step 1: Simplify both sides of the equation.
On the left side, combine like terms: $0.3x + 7.4x = 7.7x$.
Thus, the equation becomes:

$7.7x - 4.5 = 3.8x - 3.5 + 1.4$

Simplify the right side:

$3.8x - 3.5 + 1.4 = 3.8x - 2.1$

The equation now is:

$7.7x - 4.5 = 3.8x - 2.1$

Step 2: Isolate the $x$-terms on one side.
Subtract $3.8x$ from both sides to get:

$7.7x - 3.8x - 4.5 = -2.1$

Which simplifies to:

$3.9x - 4.5 = -2.1$

Now, add 4.5 to both sides to isolate the $x$-term:

$3.9x = -2.1 + 4.5$

$3.9x = 2.4$

Step 3: Solve for $x$.
Divide both sides by 3.9:

$x = \frac{2.4}{3.9}$

$x = 0.6153846153...$

Rounding to two decimal places, we find:

$x = 0.61$

Therefore, the solution to the problem is $x = 0.61$.