x−42​ ≥0 inequation

Given the inequality:
$$x - 42 \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x - 42 = 0$$
Solve:
Given the linear equation:

x-42 = 0

Move free summands (without x)
from left part to right part, we given:
$$x = 42$$
$$x_{1} = 42$$
$$x_{1} = 42$$
This roots
$$x_{1} = 42$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 42$$
=
$$\frac{419}{10}$$
substitute to the expression
$$x - 42 \geq 0$$
$$-42 + \frac{419}{10} \geq 0$$

-1/10 >= 0

but

-1/10 < 0

Then
$$x \leq 42$$
no execute
the solution of our inequality is:
$$x \geq 42$$

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