Given the inequality:
$$x + 10 > 22$$
To solve this inequality, we must first solve the corresponding equation:
$$x + 10 = 22$$
Solve:
Given the linear equation:
x+10 = 22
Move free summands (without x)
from left part to right part, we given:
$$x = 12$$
$$x_{1} = 12$$
$$x_{1} = 12$$
This roots
$$x_{1} = 12$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 12$$
=
$$\frac{119}{10}$$
substitute to the expression
$$x + 10 > 22$$
$$10 + \frac{119}{10} > 22$$
219
--- > 22
10
Then
$$x < 12$$
no execute
the solution of our inequality is:
$$x > 12$$
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