sin(4*x)/3>-3/2 inequation

Given the inequality:
$$\frac{\sin{\left(4 x \right)}}{3} > - \frac{3}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\sin{\left(4 x \right)}}{3} = - \frac{3}{2}$$
Solve:
Given the equation
$$\frac{\sin{\left(4 x \right)}}{3} = - \frac{3}{2}$$
- this is the simplest trigonometric equation

Divide both parts of the equation by 1/3

The equation is transformed to
$$\sin{\left(4 x \right)} = - \frac{9}{2}$$
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.
$$x_{1} = \frac{\pi}{4} + \frac{\operatorname{asin}{\left(\frac{9}{2} \right)}}{4}$$
$$x_{2} = - \frac{\operatorname{asin}{\left(\frac{9}{2} \right)}}{4}$$
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

$$\frac{\sin{\left(0 \cdot 4 \right)}}{3} > - \frac{3}{2}$$

0 > -3/2

so the inequality is always executed