x-27_>-16 inequation

Given the inequality:
$$x - 27 \geq -16$$
To solve this inequality, we must first solve the corresponding equation:
$$x - 27 = -16$$
Solve:
Given the linear equation:

x-27 = -16

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:
$$x_{0} \leq x_{1}$$
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
$$x - 27 \geq -16$$
$$-27 + \frac{109}{10} \geq -16$$

-161        
----- >= -16
  10        

but

-161       
----- < -16
  10       

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

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