-2cosx/3<3 inequation

Given the inequality:
$$\frac{\left(-1\right) 2 \cos{\left(x \right)}}{3} < 3$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(-1\right) 2 \cos{\left(x \right)}}{3} = 3$$
Solve:
Given the equation
$$\frac{\left(-1\right) 2 \cos{\left(x \right)}}{3} = 3$$
- this is the simplest trigonometric equation

Divide both parts of the equation by -2/3

The equation is transformed to
$$\cos{\left(x \right)} = - \frac{9}{2}$$
As right part of the equation
modulo =

True

but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$x_{1} = 2 \pi - \operatorname{acos}{\left(- \frac{9}{2} \right)}$$
$$x_{2} = \operatorname{acos}{\left(- \frac{9}{2} \right)}$$
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

$$\frac{\left(-1\right) 2 \cos{\left(0 \right)}}{3} < 3$$

-2/3 < 3

so the inequality is always executed