5-11x≤2 inequation

Given the inequality:
$$5 - 11 x \leq 2$$
To solve this inequality, we must first solve the corresponding equation:
$$5 - 11 x = 2$$
Solve:
Given the linear equation:

5-11*x = 2

Move free summands (without x)
from left part to right part, we given:
$$- 11 x = -3$$
Divide both parts of the equation by -11

x = -3 / (-11)

$$x_{1} = \frac{3}{11}$$
$$x_{1} = \frac{3}{11}$$
This roots
$$x_{1} = \frac{3}{11}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{3}{11}$$
=
$$\frac{19}{110}$$
substitute to the expression
$$5 - 11 x \leq 2$$
$$5 - \frac{11 \cdot 19}{110} \leq 2$$

31     
-- <= 2
10     

but

31     
-- >= 2
10     

Then
$$x \leq \frac{3}{11}$$
no execute
the solution of our inequality is:
$$x \geq \frac{3}{11}$$

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