sqrt(5-x)<5 inequation

Given the inequality:
$$\sqrt{5 - x} < 5$$
To solve this inequality, we must first solve the corresponding equation:
$$\sqrt{5 - x} = 5$$
Solve:
Given the equation
$$\sqrt{5 - x} = 5$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{5 - x}\right)^{2} = 5^{2}$$
or
$$5 - x = 25$$
Move free summands (without x)
from left part to right part, we given:
$$- x = 20$$
Divide both parts of the equation by -1

x = 20 / (-1)

We get the answer: x = -20

$$x_{1} = -20$$
$$x_{1} = -20$$
This roots
$$x_{1} = -20$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-20 + - \frac{1}{10}$$
=
$$- \frac{201}{10}$$
substitute to the expression
$$\sqrt{5 - x} < 5$$
$$\sqrt{5 - - \frac{201}{10}} < 5$$

  ______    
\/ 2510     
-------- < 5
   10       
    

but

  ______    
\/ 2510     
-------- > 5
   10       
    

Then
$$x < -20$$
no execute
the solution of our inequality is:
$$x > -20$$

         _____  
        /
-------ο-------
       x1