9-4x>-23 inequation

Given the inequality:
$$9 - 4 x > -23$$
To solve this inequality, we must first solve the corresponding equation:
$$9 - 4 x = -23$$
Solve:
Given the linear equation:

9-4*x = -23

Move free summands (without x)
from left part to right part, we given:
$$- 4 x = -32$$
Divide both parts of the equation by -4

x = -32 / (-4)

$$x_{1} = 8$$
$$x_{1} = 8$$
This roots
$$x_{1} = 8$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 8$$
=
$$\frac{79}{10}$$
substitute to the expression
$$9 - 4 x > -23$$
$$9 - \frac{4 \cdot 79}{10} > -23$$

-113/5 > -23

the solution of our inequality is:
$$x < 8$$

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