22x-9≤1 inequation

Given the inequality:
$$22 x - 9 \leq 1$$
To solve this inequality, we must first solve the corresponding equation:
$$22 x - 9 = 1$$
Solve:
Given the linear equation:

22*x-9 = 1

Move free summands (without x)
from left part to right part, we given:
$$22 x = 10$$
Divide both parts of the equation by 22

x = 10 / (22)

$$x_{1} = \frac{5}{11}$$
$$x_{1} = \frac{5}{11}$$
This roots
$$x_{1} = \frac{5}{11}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{5}{11}$$
=
$$\frac{39}{110}$$
substitute to the expression
$$22 x - 9 \leq 1$$
$$-9 + \frac{22 \cdot 39}{110} \leq 1$$

-6/5 <= 1

the solution of our inequality is:
$$x \leq \frac{5}{11}$$

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