5x-10(3+x)>-6 inequation

Given the inequality:
$$5 x - 10 \left(x + 3\right) > -6$$
To solve this inequality, we must first solve the corresponding equation:
$$5 x - 10 \left(x + 3\right) = -6$$
Solve:
Given the linear equation:

5*x-10*(3+x) = -6

Expand brackets in the left part

5*x-10*3-10*x = -6

Looking for similar summands in the left part:

-30 - 5*x = -6

Move free summands (without x)
from left part to right part, we given:
$$- 5 x = 24$$
Divide both parts of the equation by -5

x = 24 / (-5)

$$x_{1} = - \frac{24}{5}$$
$$x_{1} = - \frac{24}{5}$$
This roots
$$x_{1} = - \frac{24}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{24}{5} + - \frac{1}{10}$$
=
$$- \frac{49}{10}$$
substitute to the expression
$$5 x - 10 \left(x + 3\right) > -6$$
$$\frac{\left(-49\right) 5}{10} - 10 \left(- \frac{49}{10} + 3\right) > -6$$

-11/2 > -6

the solution of our inequality is:
$$x < - \frac{24}{5}$$

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