5^5-4*x-2*(1/5)^3-4*x+5>=0 inequation

Given the inequality:
$$\left(- 4 x + \left(\left(3125 - 4 x\right) - \frac{2}{125}\right)\right) + 5 \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(- 4 x + \left(\left(3125 - 4 x\right) - \frac{2}{125}\right)\right) + 5 = 0$$
Solve:
Given the linear equation:

5^5-4*x-2*(1/5)^3-4*x+5 = 0

Expand brackets in the left part

5^5-4*x-2*1/5^3-4*x+5 = 0

Looking for similar summands in the left part:

391248/125 - 8*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 8 x = - \frac{391248}{125}$$
Divide both parts of the equation by -8

x = -391248/125 / (-8)

$$x_{1} = \frac{48906}{125}$$
$$x_{1} = \frac{48906}{125}$$
This roots
$$x_{1} = \frac{48906}{125}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{48906}{125}$$
=
$$\frac{97787}{250}$$
substitute to the expression
$$\left(- 4 x + \left(\left(3125 - 4 x\right) - \frac{2}{125}\right)\right) + 5 \geq 0$$
$$\left(- \frac{4 \cdot 97787}{250} + \left(- 2 \left(\frac{1}{5}\right)^{3} + \left(3125 - \frac{4 \cdot 97787}{250}\right)\right)\right) + 5 \geq 0$$

4/5 >= 0

the solution of our inequality is:
$$x \leq \frac{48906}{125}$$

 _____          
      \    
-------•-------
       x1