5x-10(3-x)>-6 inequation

Given the inequality:
$$5 x - 10 \left(3 - x\right) > -6$$
To solve this inequality, we must first solve the corresponding equation:
$$5 x - 10 \left(3 - x\right) = -6$$
Solve:
Given the linear equation:

5*x-10*(3-x) = -6

Expand brackets in the left part

5*x-10*3+10*x = -6

Looking for similar summands in the left part:

-30 + 15*x = -6

Move free summands (without x)
from left part to right part, we given:
$$15 x = 24$$
Divide both parts of the equation by 15

x = 24 / (15)

$$x_{1} = \frac{8}{5}$$
$$x_{1} = \frac{8}{5}$$
This roots
$$x_{1} = \frac{8}{5}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{8}{5}$$
=
$$\frac{3}{2}$$
substitute to the expression
$$5 x - 10 \left(3 - x\right) > -6$$
$$- 10 \left(3 - \frac{3}{2}\right) + \frac{3 \cdot 5}{2} > -6$$

-15/2 > -6

Then
$$x < \frac{8}{5}$$
no execute
the solution of our inequality is:
$$x > \frac{8}{5}$$

         _____  
        /
-------ο-------
       x1