5-4(x-2)<22 inequation

Given the inequality:
$$5 - 4 \left(x - 2\right) < 22$$
To solve this inequality, we must first solve the corresponding equation:
$$5 - 4 \left(x - 2\right) = 22$$
Solve:
Given the linear equation:

5-4*(x-2) = 22

Expand brackets in the left part

5-4*x+4*2 = 22

Looking for similar summands in the left part:

13 - 4*x = 22

Move free summands (without x)
from left part to right part, we given:
$$- 4 x = 9$$
Divide both parts of the equation by -4

x = 9 / (-4)

$$x_{1} = - \frac{9}{4}$$
$$x_{1} = - \frac{9}{4}$$
This roots
$$x_{1} = - \frac{9}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{9}{4} + - \frac{1}{10}$$
=
$$- \frac{47}{20}$$
substitute to the expression
$$5 - 4 \left(x - 2\right) < 22$$
$$5 - 4 \left(- \frac{47}{20} - 2\right) < 22$$

112/5 < 22

but

112/5 > 22

Then
$$x < - \frac{9}{4}$$
no execute
the solution of our inequality is:
$$x > - \frac{9}{4}$$

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