-10x<-20 inequation

Given the inequality:
$$- 10 x < -20$$
To solve this inequality, we must first solve the corresponding equation:
$$- 10 x = -20$$
Solve:
Given the linear equation:

-10*x = -20

Divide both parts of the equation by -10

x = -20 / (-10)

$$x_{1} = 2$$
$$x_{1} = 2$$
This roots
$$x_{1} = 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2$$
=
$$\frac{19}{10}$$
substitute to the expression
$$- 10 x < -20$$
$$- \frac{10 \cdot 19}{10} < -20$$

-19 < -20

but

-19 > -20

Then
$$x < 2$$
no execute
the solution of our inequality is:
$$x > 2$$

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