Given the inequality:
$$- x < 20$$
To solve this inequality, we must first solve the corresponding equation:
$$- x = 20$$
Solve:
Given the linear equation:
-x = 20
Divide both parts of the equation by -1
x = 20 / (-1)
$$x_{1} = -20$$
$$x_{1} = -20$$
This roots
$$x_{1} = -20$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-20 + - \frac{1}{10}$$
=
$$- \frac{201}{10}$$
substitute to the expression
$$- x < 20$$
$$- \frac{-201}{10} < 20$$
201
--- < 20
10
but
201
--- > 20
10
Then
$$x < -20$$
no execute
the solution of our inequality is:
$$x > -20$$
_____
/
-------ο-------
x1