6*x-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:
$$- 5 x = 30$$
Divide both parts of the equation by -5

x = 30 / (-5)

$$x_{1} = -6$$
$$x_{1} = -6$$
This roots
$$x_{1} = -6$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-6 + - \frac{1}{10}$$
=
$$- \frac{61}{10}$$
substitute to the expression
$$6 x - 11 \left(x + 2\right) > 8$$
$$\frac{\left(-61\right) 6}{10} - 11 \left(- \frac{61}{10} + 2\right) > 8$$

17/2 > 8

the solution of our inequality is:
$$x < -6$$

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