3x-5 inequation

Given the inequality:
$$3 x - 5 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$3 x - 5 = 0$$
Solve:
Given the linear equation:

3*x-5 = 0

Move free summands (without x)
from left part to right part, we given:
$$3 x = 5$$
Divide both parts of the equation by 3

x = 5 / (3)

$$x_{1} = \frac{5}{3}$$
$$x_{1} = \frac{5}{3}$$
This roots
$$x_{1} = \frac{5}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{5}{3}$$
=
$$\frac{47}{30}$$
substitute to the expression
$$3 x - 5 > 0$$
$$-5 + \frac{3 \cdot 47}{30} > 0$$

-3/10 > 0

Then
$$x < \frac{5}{3}$$
no execute
the solution of our inequality is:
$$x > \frac{5}{3}$$

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