-3x+8≥5 inequation

Given the inequality:
$$8 - 3 x \geq 5$$
To solve this inequality, we must first solve the corresponding equation:
$$8 - 3 x = 5$$
Solve:
Given the linear equation:

-3*x+8 = 5

Move free summands (without x)
from left part to right part, we given:
$$- 3 x = -3$$
Divide both parts of the equation by -3

x = -3 / (-3)

$$x_{1} = 1$$
$$x_{1} = 1$$
This roots
$$x_{1} = 1$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 1$$
=
$$\frac{9}{10}$$
substitute to the expression
$$8 - 3 x \geq 5$$
$$8 - \frac{3 \cdot 9}{10} \geq 5$$

53     
-- >= 5
10     

the solution of our inequality is:
$$x \leq 1$$

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