7-9x>3 inequation

Given the inequality:
$$7 - 9 x > 3$$
To solve this inequality, we must first solve the corresponding equation:
$$7 - 9 x = 3$$
Solve:
Given the linear equation:

7-9*x = 3

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

x = -4 / (-9)

$$x_{1} = \frac{4}{9}$$
$$x_{1} = \frac{4}{9}$$
This roots
$$x_{1} = \frac{4}{9}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{4}{9}$$
=
$$\frac{31}{90}$$
substitute to the expression
$$7 - 9 x > 3$$
$$7 - \frac{9 \cdot 31}{90} > 3$$

39    
-- > 3
10    

the solution of our inequality is:
$$x < \frac{4}{9}$$

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