2/0.5√(5x)-1≥2 inequation

Given the inequality:

 2    _____         
---*\/ 5*x  - 1 >= 2
1/2                 

To solve this inequality, we must first solve the corresponding equation:

 2    _____        
---*\/ 5*x  - 1 = 2
1/2                

Solve:
Given the equation

 2    _____        
---*\/ 5*x  - 1 = 2
1/2                

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:
$$\left(4 \sqrt{5}\right)^{2} \left(\sqrt{x}\right)^{2} = 3^{2}$$
or
$$80 x = 9$$
Divide both parts of the equation by 80

x = 9 / (80)

We get the answer: x = 9/80

$$x_{1} = \frac{9}{80}$$
$$x_{1} = \frac{9}{80}$$
This roots
$$x_{1} = \frac{9}{80}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{9}{80}$$
=
$$\frac{1}{80}$$
substitute to the expression

 2    _____         
---*\/ 5*x  - 1 >= 2
1/2                 

        ____         
 2     / 5           
---*  /  --  - 1 >= 2
/1\ \/   80          
|-|                  
\2/                  

0 >= 2

but

0 < 2

Then
$$x \leq \frac{9}{80}$$
no execute
the solution of our inequality is:
$$x \geq \frac{9}{80}$$

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        /
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       x1