Question

Hey,

I forgot how to solve inequalities with modules, for example:

|x|>0 I would say the answer is (-infinity;0) and (0;+infinity), because you can take any negative number and the module would make it positive anyways

But what is about this one:

|x|>x

Answer 1

\(|x| = \pm x\)

Answer 2

Could you please explain further, @Jhannybean

Answer 3

so basically x must be negative,this way x on the right side will always be smaller than x on the left side, right?

Answer 4

the answer is (-infinity;0)?

Answer 5

Kam, you're so good at these! :D

Answer 6

Hm... Not sure how to explain this properly...but since \(|x| = \pm x\)

The only way \(|x| > x\) is if \(-x > x\)

Answer 7

but i'm not quite sure on the interval notation :\

Answer 8

your understanding is correct :)

and an alternate way to show it algebraically is

|x|> x

so, x>x or -x>x

x>x is never true

-x>x ---> -2x>0
-x>0
x<0

Answer 9

interval notation of x<0
is indeed \( (-\infty,0) \)

Answer 10

Ohh... I see I see.\[-x > x \implies -x-x>0 \implies -2x > 0 \implies x < 0\]

Now I get it!

Answer 11

good! :)

Answer 12

thank you so muchhh:}}