inequality

Solve the inequality x^3 + 4x > 5x.

x^3-x>0

x(x+2)(x-1)>0

-1x

x>1

Yay!

Hey there, Guest!

Let's find the critical points of the inequality:

$x^3+4x=5x$

$x^3+4x−5x=5x−5x$ (Subtract 5x from both sides)

$x^3−x=0$

$x(x+1)(x−1)=0$ (Factor left side of the equation)

$x=0$ or $x=-1$ or $x=1$

Check intervals in between critical points. (Test values in the intervals to see if they work.)

$x<−1$ (Doesn't work in original inequality)

\(−1  (Works in original inequality)

\(0  (Doesn't work in original inequality)

$x>1$ (Works in original inequality)

Therefore the answers to your equation are: 

−1  or  x>1

Hope this helped! :)

( ﾟдﾟ)つ Bye