Solve the linear equation $4x - 0.3 = 0.5x - 6$ for $x$.

1. Problem Description

Solve the linear equation $4x - 0.3 = 0.5x - 6$ for $x$.

2. Solution Steps

First, we want to group the $x$ terms on one side of the equation and the constant terms on the other side.

Subtract $0.5x$ from both sides of the equation:

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

$3.5x - 0.3 = -6$

Next, add $0.3$ to both sides of the equation:

$3.5x - 0.3 + 0.3 = -6 + 0.3$

$3.5x = -5.7$

Finally, divide both sides by $3.5$:

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

To simplify the fraction, we can multiply both the numerator and denominator by 10:

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

3. Final Answer

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