0,7(x-3)>0,49 inequation

Given the inequality:
$$\frac{7 \left(x - 3\right)}{10} > \frac{49}{100}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{7 \left(x - 3\right)}{10} = \frac{49}{100}$$
Solve:
Given the linear equation:

(7/10)*(x-3) = (49/100)

Expand brackets in the left part

7/10x-3 = (49/100)

Expand brackets in the right part

7/10x-3 = 49/100

Move free summands (without x)
from left part to right part, we given:
$$\frac{7 x}{10} = \frac{259}{100}$$
Divide both parts of the equation by 7/10

x = 259/100 / (7/10)

$$x_{1} = \frac{37}{10}$$
$$x_{1} = \frac{37}{10}$$
This roots
$$x_{1} = \frac{37}{10}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{37}{10}$$
=
$$\frac{18}{5}$$
substitute to the expression
$$\frac{7 \left(x - 3\right)}{10} > \frac{49}{100}$$
$$\frac{7 \left(-3 + \frac{18}{5}\right)}{10} > \frac{49}{100}$$

21    49
-- > ---
50   100

Then
$$x < \frac{37}{10}$$
no execute
the solution of our inequality is:
$$x > \frac{37}{10}$$

         _____  
        /
-------ο-------
       x1