5x-2>3 inequation

Given the inequality:
$$5 x - 2 > 3$$
To solve this inequality, we must first solve the corresponding equation:
$$5 x - 2 = 3$$
Solve:
Given the linear equation:

5*x-2 = 3

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

x = 5 / (5)

$$x_{1} = 1$$
$$x_{1} = 1$$
This roots
$$x_{1} = 1$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 1$$
=
$$\frac{9}{10}$$
substitute to the expression
$$5 x - 2 > 3$$
$$-2 + \frac{5 \cdot 9}{10} > 3$$

5/2 > 3

Then
$$x < 1$$
no execute
the solution of our inequality is:
$$x > 1$$

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