-2cosx/3

+ inequation

Solve the inequality!

A inequation with variable

The solution

You have entered [src]

-2*cos(x)   3 ___
--------- < \/ 3 
    3            

$$\frac{\left(-1\right) 2 \cos{\left(x \right)}}{3} < \sqrt[3]{3}$$

(-2*cos(x))/3 < 3^(1/3)

Detail solution

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

Divide both parts of the equation by -2/3

The equation is transformed to
$$\cos{\left(x \right)} = - \frac{3 \sqrt[3]{3}}{2}$$
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.
$$x_{1} = 2 \pi - \operatorname{acos}{\left(- \frac{3 \sqrt[3]{3}}{2} \right)}$$
$$x_{2} = \operatorname{acos}{\left(- \frac{3 \sqrt[3]{3}}{2} \right)}$$
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

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

       3 ___
-2/3 < \/ 3 
       

so the inequality is always executed

Solving inequality on a graph

Rapid solution 2 [src]

(-oo, oo)

$$x\ in\ \left(-\infty, \infty\right)$$

x in Interval(-oo, oo)

Rapid solution [src]

And(-oo < x, x < oo)

$$-\infty < x \wedge x < \infty$$

(-oo < x)∧(x < oo)