2/17+x≥0 inequation

Given the inequality:
$$x + \frac{2}{17} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x + \frac{2}{17} = 0$$
Solve:
Given the linear equation:

2/17+x = 0

Move free summands (without x)
from left part to right part, we given:
$$x = - \frac{2}{17}$$
$$x_{1} = - \frac{2}{17}$$
$$x_{1} = - \frac{2}{17}$$
This roots
$$x_{1} = - \frac{2}{17}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{2}{17} + - \frac{1}{10}$$
=
$$- \frac{37}{170}$$
substitute to the expression
$$x + \frac{2}{17} \geq 0$$
$$- \frac{37}{170} + \frac{2}{17} \geq 0$$

-1/10 >= 0

but

-1/10 < 0

Then
$$x \leq - \frac{2}{17}$$
no execute
the solution of our inequality is:
$$x \geq - \frac{2}{17}$$

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