90-1/3x>91 inequation

Given the inequality:
$$90 - \frac{x}{3} > 91$$
To solve this inequality, we must first solve the corresponding equation:
$$90 - \frac{x}{3} = 91$$
Solve:
Given the linear equation:

90-1/3*x = 91

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

x = 1 / (-1/3)

$$x_{1} = -3$$
$$x_{1} = -3$$
This roots
$$x_{1} = -3$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-3 + - \frac{1}{10}$$
=
$$- \frac{31}{10}$$
substitute to the expression
$$90 - \frac{x}{3} > 91$$
$$90 - \frac{-31}{3 \cdot 10} > 91$$

2731     
---- > 91
 30      

the solution of our inequality is:
$$x < -3$$

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