3x+12≥6x inequation

Given the inequality:
$$3 x + 12 \geq 6 x$$
To solve this inequality, we must first solve the corresponding equation:
$$3 x + 12 = 6 x$$
Solve:
Given the linear equation:

3*x+12 = 6*x

Move free summands (without x)
from left part to right part, we given:
$$3 x = 6 x - 12$$
Move the summands with the unknown x
from the right part to the left part:
$$- 3 x = -12$$
Divide both parts of the equation by -3

x = -12 / (-3)

$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$3 x + 12 \geq 6 x$$
$$3 \cdot \frac{39}{10} + 12 \geq 6 \cdot \frac{39}{10}$$

237         
--- >= 117/5
 10         

the solution of our inequality is:
$$x \leq 4$$

 _____          
      \    
-------•-------
       x_1