1−3x≤0 inequation

Given the inequality:
$$1 - 3 x \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$1 - 3 x = 0$$
Solve:
Given the linear equation:

1-3*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 3 x = -1$$
Divide both parts of the equation by -3

x = -1 / (-3)

$$x_{1} = \frac{1}{3}$$
$$x_{1} = \frac{1}{3}$$
This roots
$$x_{1} = \frac{1}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{3}$$
=
$$\frac{7}{30}$$
substitute to the expression
$$1 - 3 x \leq 0$$
$$1 - \frac{3 \cdot 7}{30} \leq 0$$

3/10 <= 0

but

3/10 >= 0

Then
$$x \leq \frac{1}{3}$$
no execute
the solution of our inequality is:
$$x \geq \frac{1}{3}$$

         _____  
        /
-------•-------
       x1