Question

Steven conjectures that for |x|>5, it is true that x^3>125. Is his conjecture correct? Why or why not?

Answer 1

Conjectures are conclusions formed from evidences. Steven's conjecture that: $x^3 > 125$ is true because: $x > 5$ or $x > -5$ for $|x| > 5$

Given that:

$|x| > 5$

Split the inequality as follows:

$x > 5$ or $x > -5$

Take the cube of both sides

$x^3 > 5^3$ or $x^3 > -5^3$

Evaluate all exponents

$x^3 > 125$ or $x^3 > -125$

Steven's conjecture that: $x^3 > 125$ is true because:

$x > 5$ or $x > -5$ for $|x| > 5$

Read more about absolute inequalities at:

brainly.com/question/4688732