2x-1:5-x>_0 inequation

Given the inequality:
$$- x + \left(2 x - \frac{1}{5}\right) \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- x + \left(2 x - \frac{1}{5}\right) = 0$$
Solve:
Given the linear equation:

2*x-1/5-x = 0

Looking for similar summands in the left part:

-1/5 + x = 0

Move free summands (without x)
from left part to right part, we given:
$$x = \frac{1}{5}$$
$$x_{1} = \frac{1}{5}$$
$$x_{1} = \frac{1}{5}$$
This roots
$$x_{1} = \frac{1}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{5}$$
=
$$\frac{1}{10}$$
substitute to the expression
$$- x + \left(2 x - \frac{1}{5}\right) \geq 0$$
$$- \frac{1}{10} + \left(- \frac{1}{5} + \frac{2}{10}\right) \geq 0$$

-1/10 >= 0

but

-1/10 < 0

Then
$$x \leq \frac{1}{5}$$
no execute
the solution of our inequality is:
$$x \geq \frac{1}{5}$$

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