sin7x>sqrt(3/2) inequation

Given the inequality:
$$\sin{\left(7 x \right)} > \sqrt{\frac{3}{2}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(7 x \right)} = \sqrt{\frac{3}{2}}$$
Solve:
Given the equation
$$\sin{\left(7 x \right)} = \sqrt{\frac{3}{2}}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =

True

but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$x_{1} = \frac{\pi}{7} - \frac{\operatorname{asin}{\left(\frac{\sqrt{6}}{2} \right)}}{7}$$
$$x_{2} = \frac{\operatorname{asin}{\left(\frac{\sqrt{6}}{2} \right)}}{7}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example

x0 = 0

$$\sin{\left(0 \cdot 7 \right)} > \sqrt{\frac{3}{2}}$$

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    \/ 6 
0 > -----
      2  
    

so the inequality has no solutions