6x-11(x+2)>-8 inequation

Given the inequality:
$$6 x - 11 \left(x + 2\right) > -8$$
To solve this inequality, we must first solve the corresponding equation:
$$6 x - 11 \left(x + 2\right) = -8$$
Solve:
Given the linear equation:

6*x-11*(x+2) = -8

Expand brackets in the left part

6*x-11*x-11*2 = -8

Looking for similar summands in the left part:

-22 - 5*x = -8

Move free summands (without x)
from left part to right part, we given:
$$- 5 x = 14$$
Divide both parts of the equation by -5

x = 14 / (-5)

$$x_{1} = - \frac{14}{5}$$
$$x_{1} = - \frac{14}{5}$$
This roots
$$x_{1} = - \frac{14}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{14}{5} + - \frac{1}{10}$$
=
$$- \frac{29}{10}$$
substitute to the expression
$$6 x - 11 \left(x + 2\right) > -8$$
$$\frac{\left(-29\right) 6}{10} - 11 \left(- \frac{29}{10} + 2\right) > -8$$

-15/2 > -8

the solution of our inequality is:
$$x < - \frac{14}{5}$$

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