3x-15≥21 inequation

Given the inequality:
$$3 x - 15 \geq 21$$
To solve this inequality, we must first solve the corresponding equation:
$$3 x - 15 = 21$$
Solve:
Given the linear equation:

3*x-15 = 21

Move free summands (without x)
from left part to right part, we given:
$$3 x = 36$$
Divide both parts of the equation by 3

x = 36 / (3)

$$x_{1} = 12$$
$$x_{1} = 12$$
This roots
$$x_{1} = 12$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 12$$
=
$$\frac{119}{10}$$
substitute to the expression
$$3 x - 15 \geq 21$$
$$-15 + \frac{3 \cdot 119}{10} \geq 21$$

207      
--- >= 21
 10      

but

207     
--- < 21
 10     

Then
$$x \leq 12$$
no execute
the solution of our inequality is:
$$x \geq 12$$

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