x+1>9 inequation

Given the inequality:
$$x + 1 > 9$$
To solve this inequality, we must first solve the corresponding equation:
$$x + 1 = 9$$
Solve:
Given the linear equation:

x+1 = 9

Move free summands (without x)
from left part to right part, we given:
$$x = 8$$
$$x_{1} = 8$$
$$x_{1} = 8$$
This roots
$$x_{1} = 8$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 8$$
=
$$\frac{79}{10}$$
substitute to the expression
$$x + 1 > 9$$
$$1 + \frac{79}{10} > 9$$

89    
-- > 9
10    

Then
$$x < 8$$
no execute
the solution of our inequality is:
$$x > 8$$

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