x-2<9 inequation

Given the inequality:
$$x - 2 < 9$$
To solve this inequality, we must first solve the corresponding equation:
$$x - 2 = 9$$
Solve:
Given the linear equation:

x-2 = 9

Move free summands (without x)
from left part to right part, we given:
$$x = 11$$
$$x_{1} = 11$$
$$x_{1} = 11$$
This roots
$$x_{1} = 11$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 11$$
=
$$\frac{109}{10}$$
substitute to the expression
$$x - 2 < 9$$
$$-2 + \frac{109}{10} < 9$$

89    
-- < 9
10    

the solution of our inequality is:
$$x < 11$$

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