Answer:
Incorrect
Step-by-step explanation:
Given
[tex]x < -1[/tex]
[tex]x^5 - 2 > x[/tex]
Required
Determine if the conjecture is true
To determine if it's true or not, we have to substitute the values of x in [tex]x^5 - 2 > x[/tex]
In the first inequality, we have that [tex]x < -1[/tex]
This means that the values of x are: -2. -3, -4......
Substitute -2 for x in [tex]x^5 - 2 > x[/tex]
[tex](-2)^5 - 2 > -2[/tex]
[tex]-32 - 2 > -2[/tex]
[tex]-34 > -2[/tex]
Her conjecture is incorrect because the inequality is not true for x = -2
