Solve for X: Finding X in 1/4x + 0.3 - 0.1 = 3/4x - 0.8

To solve this linear equation, we follow these steps:

• Step 1: Simplify both sides of the equation by combining constants.
• Step 2: Move terms with $x$ to one side of the equation and constants to the other.
• Step 3: Solve for $x$ by isolating it.

Let's proceed:

First, simplify the left side of the equation by combining the constants $0.3$ and $-0.1$:

$\frac{1}{4}x + 0.3 - 0.1 = \frac{1}{4}x + 0.2$

So the equation becomes:

$\frac{1}{4}x + 0.2 = \frac{3}{4}x - 0.8$

Next, we move the terms involving $x$ to one side. Subtract $\frac{1}{4}x$ from both sides:

$0.2 = \frac{3}{4}x - \frac{1}{4}x - 0.8$

This simplifies to:

$0.2 = \frac{2}{4}x - 0.8$

which simplifies further to:

$0.2 = \frac{1}{2}x - 0.8$

Now, isolate $\frac{1}{2}x$ by adding $0.8$ to both sides:

$0.2 + 0.8 = \frac{1}{2}x$

This gives:

$1.0 = \frac{1}{2}x$

To solve for $x$, multiply both sides by 2:

$x = 2 \times 1.0$

Therefore,

$x = 2$

Hence, the correct answer is $x = 2$.