3-18*x<0 inequation

Given the inequality:
$$3 - 18 x < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$3 - 18 x = 0$$
Solve:
Given the linear equation:

3-18*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 18 x = -3$$
Divide both parts of the equation by -18

x = -3 / (-18)

$$x_{1} = \frac{1}{6}$$
$$x_{1} = \frac{1}{6}$$
This roots
$$x_{1} = \frac{1}{6}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{6}$$
=
$$\frac{1}{15}$$
substitute to the expression
$$3 - 18 x < 0$$
$$3 - \frac{18}{15} < 0$$

9/5 < 0

but

9/5 > 0

Then
$$x < \frac{1}{6}$$
no execute
the solution of our inequality is:
$$x > \frac{1}{6}$$

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