Solve for X: (10x-1/5)·1/2 = -1/10+8x Linear Equation

To solve this problem, we'll proceed step-by-step:

First, we distribute the $\frac{1}{2}$ across the term inside the parentheses:
$\frac{1}{2} \cdot (10x - \frac{1}{5}) = \frac{1}{2} \cdot 10x - \frac{1}{2} \cdot \frac{1}{5}$.

This simplifies to:
$5x - \frac{1}{10}$.

Now, our equation becomes:
$5x - \frac{1}{10} = -\frac{1}{10} + 8x$.

Next, we aim to gather the $x$ terms on one side. Subtract $5x$ from both sides:
$-\frac{1}{10} = -\frac{1}{10} + 8x - 5x$.

Simplify the right-hand side:
$-\frac{1}{10} = -\frac{1}{10} + 3x$.

To isolate $3x$, subtract $-\frac{1}{10}$ from both sides:
$0 = 3x$.

Divide both sides by 3 to solve for $x$:
$x = 0$.

Therefore, the solution to the problem is $x = 0$.