-1/24x<5/6 inequation

Given the inequality:
$$- \frac{x}{24} < \frac{5}{6}$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{x}{24} = \frac{5}{6}$$
Solve:
Given the linear equation:

-1/24*x = 5/6

Divide both parts of the equation by -1/24

x = 5/6 / (-1/24)

$$x_{1} = -20$$
$$x_{1} = -20$$
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
$$- \frac{x}{24} < \frac{5}{6}$$
$$- \frac{-201}{10 \cdot 24} < \frac{5}{6}$$

67      
-- < 5/6
80      

but

67      
-- > 5/6
80      

Then
$$x < -20$$
no execute
the solution of our inequality is:
$$x > -20$$

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