-8*x-16<0 inequation

Given the inequality:
$$- 8 x - 16 < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- 8 x - 16 = 0$$
Solve:
Given the linear equation:

-8*x-16 = 0

Move free summands (without x)
from left part to right part, we given:
$$- 8 x = 16$$
Divide both parts of the equation by -8

x = 16 / (-8)

$$x_{1} = -2$$
$$x_{1} = -2$$
This roots
$$x_{1} = -2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 + - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$- 8 x - 16 < 0$$
$$-16 - \frac{\left(-21\right) 8}{10} < 0$$

4/5 < 0

but

4/5 > 0

Then
$$x < -2$$
no execute
the solution of our inequality is:
$$x > -2$$

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