We have two linear equations to solve for $x$. The first equation is $-0.4x - 3 = -0.2 + 8x$. The second equation is $4x - 0.3 = 0.5x - 6$.

1. Problem Description

We have two linear equations to solve for $x$.

The first equation is $-0.4x - 3 = -0.2 + 8x$.

The second equation is $4x - 0.3 = 0.5x - 6$.

2. Solution Steps

e)

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

Add $0.4x$ to both sides:

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

$-3 = -0.2 + 8.4x$

Add $0.2$ to both sides:

$-3 + 0.2 = 8.4x$

$-2.8 = 8.4x$

Divide both sides by $8.4$:

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

$x = -\frac{28}{84}$

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

f)

$4x - 0.3 = 0.5x - 6$

Subtract $0.5x$ from both sides:

$4x - 0.5x - 0.3 = -6$

$3.5x - 0.3 = -6$

Add $0.3$ to both sides:

$3.5x = -6 + 0.3$

$3.5x = -5.7$

Divide both sides by $3.5$:

$x = \frac{-5.7}{3.5}$

$x = -\frac{57}{35}$

3. Final Answer

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

f) $x = -\frac{57}{35}$