Conjectures are conclusions formed from evidences.
Steven's conjecture that: [tex]x^3 > 125[/tex] is true because: [tex]x > 5[/tex] or [tex]x > -5[/tex] for [tex]|x| > 5[/tex]
The parameter is given as:
[tex]|x| > 5[/tex]
Split the inequality as follows:
[tex]x > 5[/tex] or [tex]x > -5[/tex]
Take the cube of both sides
[tex]x^3 > 5^3[/tex] or [tex]x^3 > -5^3[/tex]
Evaluate all exponents
[tex]x^3 > 125[/tex] or [tex]x^3 > -125[/tex]
[tex]x^3 > 125[/tex] implies that Steven's conjecture is correct.
So:
Steven's conjecture that: [tex]x^3 > 125[/tex] is true because:
[tex]x > 5[/tex] or [tex]x > -5[/tex] for [tex]|x| > 5[/tex]
Read more about absolute inequalities at:
https://brainly.com/question/4688732
