8-2x inequation

Given the inequality:
$$8 - 2 x > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$8 - 2 x = 0$$
Solve:
Given the linear equation:

8-2*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 2 x = -8$$
Divide both parts of the equation by -2

x = -8 / (-2)

$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$8 - 2 x > 0$$
$$8 - \frac{2 \cdot 39}{10} > 0$$

1/5 > 0

the solution of our inequality is:
$$x < 4$$

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