-x+3x-8>=0 inequation

Given the inequality:
$$\left(- x + 3 x\right) - 8 \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(- x + 3 x\right) - 8 = 0$$
Solve:
Given the linear equation:

-x+3*x-8 = 0

Looking for similar summands in the left part:

-8 + 2*x = 0

Move free summands (without x)
from left part to right part, we given:
$$2 x = 8$$
Divide both parts of the equation by 2

x = 8 / (2)

$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$\left(- x + 3 x\right) - 8 \geq 0$$
$$-8 + \left(- \frac{39}{10} + \frac{3 \cdot 39}{10}\right) \geq 0$$

-1/5 >= 0

but

-1/5 < 0

Then
$$x \leq 4$$
no execute
the solution of our inequality is:
$$x \geq 4$$

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