Question

x^3 > x
Solve the inequality in terms of intervals. interval notation

Answer 1

This is how I viewed the problem. Looking at this, as long as X is greater than 1 it should be true, but im getting the wrong answer. Please help?

Answer 2

Well if you're multiplying two terms together, what must their signs be for the answer to be positive?

Answer 3

Two positive or two negative?

Answer 4

Exactly. So either both x^2 and (x-1) have to be positive or they both have to be negative.

Let's start with x^2. What's the sign of x^2?

Answer 5

positive

Answer 6

Right, x^2 is always positive. So now we only care about the case where they're both positive since it's impossible for them both to be negative. So we want x-1 to be positive. Can you solve for that?

Answer 7

as long as x is greater than one

Answer 8

But the solution isn't (1,infinity) I'm confused

Answer 9

The answer is definitely x>1, or ]1,inf[

Answer 10

Not including 1 right?

Answer 11

not including, because it's asking values greater than 0

Answer 12

Well x>1 should be the right answer, I'm not sure what else to say

Answer 13

OOOHHHHH you did your factoring wrong! Sorry I missed that!

x^3 > x
x^3 - x >0
x(x^2-1) > 0
x(x-1)(x+1) > 0