x-3 inequation

Given the inequality:
$$x - 3 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x - 3 = 0$$
Solve:
Given the linear equation:

x-3 = 0

Move free summands (without x)
from left part to right part, we given:
$$x = 3$$
$$x_{1} = 3$$
$$x_{1} = 3$$
This roots
$$x_{1} = 3$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 3$$
=
$$\frac{29}{10}$$
substitute to the expression
$$x - 3 > 0$$
$$-3 + \frac{29}{10} > 0$$

-1/10 > 0

Then
$$x < 3$$
no execute
the solution of our inequality is:
$$x > 3$$

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