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)`

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)`