We are asked to solve the linear equation $-0.4x - 3 = -0.2 + 8x$ for $x$.

1. Problem Description

We are asked to solve the linear equation $-0.4x - 3 = -0.2 + 8x$ for $x$.

2. Solution Steps

We want to isolate $x$ on one side of the equation.

First, add $0.4x$ to both sides of the equation:

$-0.4x - 3 + 0.4x = -0.2 + 8x + 0.4x$

$-3 = -0.2 + 8.4x$

Next, add $0.2$ to both sides of the equation:

$-3 + 0.2 = -0.2 + 8.4x + 0.2$

$-2.8 = 8.4x$

Now, divide both sides of the equation by $8.4$ to solve for $x$:

$\frac{-2.8}{8.4} = \frac{8.4x}{8.4}$

$x = \frac{-2.8}{8.4}$

We can simplify the fraction by dividing both numerator and denominator by 2.8:

$x = \frac{-2.8}{8.4} = \frac{-1}{3}$

3. Final Answer

$x = -\frac{1}{3}$