3-4x>=11 inequation

Given the inequality:
$$3 - 4 x \geq 11$$
To solve this inequality, we must first solve the corresponding equation:
$$3 - 4 x = 11$$
Solve:
Given the linear equation:

3-4*x = 11

Move free summands (without x)
from left part to right part, we given:
$$- 4 x = 8$$
Divide both parts of the equation by -4

x = 8 / (-4)

$$x_{1} = -2$$
$$x_{1} = -2$$
This roots
$$x_{1} = -2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$3 - 4 x \geq 11$$
$$3 - 4 \left(- \frac{21}{10}\right) \geq 11$$

57/5 >= 11

the solution of our inequality is:
$$x \leq -2$$

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