5x+3>2x-6 inequation

Given the inequality:
$$5 x + 3 > 2 x - 6$$
To solve this inequality, we must first solve the corresponding equation:
$$5 x + 3 = 2 x - 6$$
Solve:
Given the linear equation:

5*x+3 = 2*x-6

Move free summands (without x)
from left part to right part, we given:
$$5 x = 2 x - 9$$
Move the summands with the unknown x
from the right part to the left part:
$$3 x = -9$$
Divide both parts of the equation by 3

x = -9 / (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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-3 - \frac{1}{10}$$
=
$$- \frac{31}{10}$$
substitute to the expression
$$5 x + 3 > 2 x - 6$$
$$5 \left(- \frac{31}{10}\right) + 3 > 2 \left(- \frac{31}{10}\right) - 6$$

-25/2 > -61/5

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

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