0,3x-20<0 inequation

Given the inequality:
$$\frac{3 x}{10} - 20 < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{3 x}{10} - 20 = 0$$
Solve:
Given the linear equation:

(3/10)*x-20 = 0

Expand brackets in the left part

3/10x-20 = 0

Move free summands (without x)
from left part to right part, we given:
$$\frac{3 x}{10} = 20$$
Divide both parts of the equation by 3/10

x = 20 / (3/10)

$$x_{1} = \frac{200}{3}$$
$$x_{1} = \frac{200}{3}$$
This roots
$$x_{1} = \frac{200}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{200}{3}$$
=
$$\frac{1997}{30}$$
substitute to the expression
$$\frac{3 x}{10} - 20 < 0$$
$$-20 + \frac{3 \cdot 1997}{10 \cdot 30} < 0$$

-3/100 < 0

the solution of our inequality is:
$$x < \frac{200}{3}$$

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