(7-9*x)/3>1 inequation

Given the inequality:
$$\frac{7 - 9 x}{3} > 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{7 - 9 x}{3} = 1$$
Solve:
Given the linear equation:

(7-9*x)/3 = 1

Expand brackets in the left part

7/3-9*x/3 = 1

Move free summands (without x)
from left part to right part, we given:
$$- 3 x = - \frac{4}{3}$$
Divide both parts of the equation by -3

x = -4/3 / (-3)

$$x_{1} = \frac{4}{9}$$
$$x_{1} = \frac{4}{9}$$
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
$$\frac{7 - 9 x}{3} > 1$$
$$\frac{7 - \frac{9 \cdot 31}{90}}{3} > 1$$

13    
-- > 1
10    

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

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