Solve the inequality below and write down the integral values that satisfy the equality

Divide by $-4$ and reverse the inequality sign:

Divide by 3:

The combined inequality is $-1 < x \le \frac{11}{3}$.
Since $\frac{11}{3} \approx 3.67$, the integral values (integers) that satisfy this condition are those greater than $-1$ and less than or equal to 3.67.
The integral values are $\boxed{0, 1, 2, 3}$.

10. Find the equation of a line which passes through the point $(2, 3)$ and is perpendicular to $y - 3x + 1 = 0$, giving your answer in the form $y = mx + c$.

The given equation is $y - 3x + 1 = 0$.
Rearrange it into the form $y = mx + c$:

The slope of this line, $m_1$, is 3.

For two lines to be perpendicular, the product of their slopes must be $-1$.
Let $m_2$ be the slope of the required line.

The line passes through $(x_1, y_1) = (2, 3)$ and has a slope $m_2 = -\frac{1}{3}$.
The point-slope form is $y - y_1 = m(x - x_1)$.

The equation of the line is $\boxed{y = -\frac{1}{3}x + \frac{11}{3}}$.