Solve for X: 5.4x + 1/5 - 3/10 = 6.4x - 2/5 Linear Equation

To solve this problem, we will follow these steps:

• Step 1: Move all terms involving $x$ to one side of the equation and constants to the other.
• Step 2: Solve for $x$ by simplifying both sides.
• Step 3: Identify the solution among the given choices.

Let's begin:

Step 1: Move the terms involving $x$ to one side of the equation:

$5.4x + \frac{1}{5} - \frac{3}{10} = 6.4x - \frac{2}{5}$

Subtract $5.4x$ and add $\frac{2}{5}$ to both sides:

$\frac{1}{5} - \frac{3}{10} + \frac{2}{5} = 6.4x - 5.4x$

Simplify:

Step 2: Combine like terms:

The left side becomes:

$\frac{1}{5} + \frac{2}{5} - \frac{3}{10}$

Convert fractions to have the same denominator:

• $\frac{1}{5} = \frac{2}{10}$
• $\frac{2}{5} = \frac{4}{10}$

Combine the terms:

$\frac{2}{10} + \frac{4}{10} - \frac{3}{10} = \frac{3}{10}$

The right side becomes:

$1x = x$

Step 3: Set the simplified terms equal to each other:

$\frac{3}{10} = x$

Therefore, the solution to the problem is $x = \frac{3}{10}$, which corresponds to choice .