(0,3)^7+4x>0,027 inequation

Given the inequality:
$$4 x + \left(\frac{3}{10}\right)^{7} > \frac{27}{1000}$$
To solve this inequality, we must first solve the corresponding equation:
$$4 x + \left(\frac{3}{10}\right)^{7} = \frac{27}{1000}$$
Solve:
Given the linear equation:

((3/10))^7+4*x = (27/1000)

Expand brackets in the left part

3/10)^7+4*x = (27/1000)

Expand brackets in the right part

3/10)^7+4*x = 27/1000

Move free summands (without x)
from left part to right part, we given:
$$4 x = \frac{267813}{10000000}$$
Divide both parts of the equation by 4

x = 267813/10000000 / (4)

$$x_{1} = \frac{267813}{40000000}$$
$$x_{1} = \frac{267813}{40000000}$$
This roots
$$x_{1} = \frac{267813}{40000000}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{267813}{40000000}$$
=
$$- \frac{3732187}{40000000}$$
substitute to the expression
$$4 x + \left(\frac{3}{10}\right)^{7} > \frac{27}{1000}$$
$$\frac{\left(-3732187\right) 4}{40000000} + \left(\frac{3}{10}\right)^{7} > \frac{27}{1000}$$

-373     27 
----- > ----
 1000   1000

Then
$$x < \frac{267813}{40000000}$$
no execute
the solution of our inequality is:
$$x > \frac{267813}{40000000}$$

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