3×sinx/4>=2 inequation

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

Divide both parts of the equation by 3/4

The equation is transformed to
$$\sin{\left(x \right)} = \frac{8}{3}$$
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.
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{8}{3} \right)}$$
$$x_{2} = \operatorname{asin}{\left(\frac{8}{3} \right)}$$
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

$$\frac{3 \sin{\left(0 \right)}}{4} \geq 2$$

0 >= 2

but

0 < 2

so the inequality has no solutions