10-4x<=2 inequation

Given the inequality:
$$10 - 4 x \leq 2$$
To solve this inequality, we must first solve the corresponding equation:
$$10 - 4 x = 2$$
Solve:
Given the linear equation:

10-4*x = 2

Move free summands (without x)
from left part to right part, we given:
$$- 4 x = -8$$
Divide both parts of the equation by -4

x = -8 / (-4)

$$x_{1} = 2$$
$$x_{1} = 2$$
This roots
$$x_{1} = 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2$$
=
$$\frac{19}{10}$$
substitute to the expression
$$10 - 4 x \leq 2$$
$$10 - \frac{4 \cdot 19}{10} \leq 2$$

12/5 <= 2

but

12/5 >= 2

Then
$$x \leq 2$$
no execute
the solution of our inequality is:
$$x \geq 2$$

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