Question

Samantha conjectures that for x < - 1 it is true that x ^ 5 - 2 > x her conjecture correct? Why or why not?

Answer 1

Incorrect

Explanation:

Given

`x < -1`

`x^5 - 2 > x`

Required

Determine if the conjecture is true

To determine if it's true or not, we have to substitute the values of x in
`x^5 - 2 > x`

In the first inequality, we have that
`x < -1`

This means that the values of x are: -2. -3, -4......

Substitute -2 for x in
`x^5 - 2 > x`

`(-2)^5 - 2 > -2`

`-32 - 2 > -2`

`-34 > -2`

Her conjecture is incorrect because the inequality is not true for x = -2