4-7(x+3)=<-9 inequation

Given the inequality:
$$4 - 7 \left(x + 3\right) \leq -9$$
To solve this inequality, we must first solve the corresponding equation:
$$4 - 7 \left(x + 3\right) = -9$$
Solve:
Given the linear equation:

4-7*(x+3) = -9

Expand brackets in the left part

4-7*x-7*3 = -9

Looking for similar summands in the left part:

-17 - 7*x = -9

Move free summands (without x)
from left part to right part, we given:
$$- 7 x = 8$$
Divide both parts of the equation by -7

x = 8 / (-7)

$$x_{1} = - \frac{8}{7}$$
$$x_{1} = - \frac{8}{7}$$
This roots
$$x_{1} = - \frac{8}{7}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{8}{7} + - \frac{1}{10}$$
=
$$- \frac{87}{70}$$
substitute to the expression
$$4 - 7 \left(x + 3\right) \leq -9$$
$$4 - 7 \left(- \frac{87}{70} + 3\right) \leq -9$$

-83       
---- <= -9
 10       

but

-83       
---- >= -9
 10       

Then
$$x \leq - \frac{8}{7}$$
no execute
the solution of our inequality is:
$$x \geq - \frac{8}{7}$$

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