-5x-10<=-6 inequation

Given the inequality:
$$- 5 x - 10 \leq -6$$
To solve this inequality, we must first solve the corresponding equation:
$$- 5 x - 10 = -6$$
Solve:
Given the linear equation:

-5*x-10 = -6

Move free summands (without x)
from left part to right part, we given:
$$- 5 x = 4$$
Divide both parts of the equation by -5

x = 4 / (-5)

$$x_{1} = - \frac{4}{5}$$
$$x_{1} = - \frac{4}{5}$$
This roots
$$x_{1} = - \frac{4}{5}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{4}{5} + - \frac{1}{10}$$
=
$$- \frac{9}{10}$$
substitute to the expression
$$- 5 x - 10 \leq -6$$
$$-10 - \frac{\left(-9\right) 5}{10} \leq -6$$

-11/2 <= -6

but

-11/2 >= -6

Then
$$x \leq - \frac{4}{5}$$
no execute
the solution of our inequality is:
$$x \geq - \frac{4}{5}$$

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