The problem is to solve the equation $-0.4x - 3 = 0.2 + 8x$ for $x$.

1. Problem Description

The problem is to solve the 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, subtract $0.2$ from both sides of the equation:

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

$-3.2 = 8.4x$

Now, divide both sides by $8.4$:

$\frac{-3.2}{8.4} = \frac{8.4x}{8.4}$

$x = \frac{-3.2}{8.4}$

We can simplify the fraction by multiplying both the numerator and the denominator by 10:

$x = \frac{-32}{84}$

Now, we can further simplify the fraction by dividing both numerator and denominator by 4:

$x = \frac{-8}{21}$

3. Final Answer

$x = -\frac{8}{21}$