Question

Solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.​

Answer 1

Answer: $x\in (0,1)\cup (4,\infty)$

Step-by-step explanation:

Given

In equality is $x^3+4x>5x^2$

Taking terms one side

$\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0$

Using wavy curve method

$x\in (0,1)\cup (4,\infty)$