-5x-6 inequation

Given the inequality:
$$- 5 x - 6 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- 5 x - 6 = 0$$
Solve:
Given the linear equation:

-5*x-6 = 0

Move free summands (without x)
from left part to right part, we given:
$$- 5 x = 6$$
Divide both parts of the equation by -5

x = 6 / (-5)

$$x_{1} = - \frac{6}{5}$$
$$x_{1} = - \frac{6}{5}$$
This roots
$$x_{1} = - \frac{6}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{6}{5} + - \frac{1}{10}$$
=
$$- \frac{13}{10}$$
substitute to the expression
$$- 5 x - 6 > 0$$
$$-6 - \frac{\left(-13\right) 5}{10} > 0$$

1/2 > 0

the solution of our inequality is:
$$x < - \frac{6}{5}$$

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