-3sin(x)<=6 inequation

Given the inequality:
$$- 3 \sin{\left(x \right)} \leq 6$$
To solve this inequality, we must first solve the corresponding equation:
$$- 3 \sin{\left(x \right)} = 6$$
Solve:
Given the equation
$$- 3 \sin{\left(x \right)} = 6$$
- this is the simplest trigonometric equation

Divide both parts of the equation by -3

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

$$- 3 \sin{\left(0 \right)} \leq 6$$

0 <= 6

so the inequality is always executed