-6x-8+x-13>0 inequation

Given the inequality:
$$\left(x + \left(- 6 x - 8\right)\right) - 13 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(x + \left(- 6 x - 8\right)\right) - 13 = 0$$
Solve:
Given the linear equation:

-6*x-8+x-13 = 0

Looking for similar summands in the left part:

-21 - 5*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 5 x = 21$$
Divide both parts of the equation by -5

x = 21 / (-5)

$$x_{1} = - \frac{21}{5}$$
$$x_{1} = - \frac{21}{5}$$
This roots
$$x_{1} = - \frac{21}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{21}{5} + - \frac{1}{10}$$
=
$$- \frac{43}{10}$$
substitute to the expression
$$\left(x + \left(- 6 x - 8\right)\right) - 13 > 0$$
$$-13 + \left(- \frac{43}{10} + \left(-8 - \frac{\left(-43\right) 6}{10}\right)\right) > 0$$

1/2 > 0

the solution of our inequality is:
$$x < - \frac{21}{5}$$

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