Question

Find the possible values of x that satisfies the inequaty |x²-1|<=|x|

Answer 1

answer is x<-17

-16-18>18+2x-18

-34>2x divide both sides by 2 and you get the answer

Answer 2

Sorry?

Answer 3

oops sorry

Answer 4

Thats not correct.

Answer 5

Do you know the absolute value laws?

Answer 6

it is what is up there

Answer 7

absolute value laws state that
x = x if x>= 0 (If x is positive)
and
x = -x if x<0 (If x is negative)

Answer 8

ok

Answer 9

but tell me how can i solve this problem? may I do first -x<= x²-1<=x

Answer 10

than -x+1<=x²<=x+1 and now?

Answer 11

no, I am going to write it out for you
wait 2min

Answer 12

ok

Answer 13

constructing our laws:

\[x^2-1 = x^2-1\] when \[x \ge 1\]

\[x^2-1 = -(x^2-1)\] when \[x \lt 1\]

Answer 14

\[x = x\] when \[x \ge 0\]

and

\[x = -x\] when \[x \lt 0\]

Answer 15

do you understand so far? we are just setting up our laws.

Answer 16

ok

Answer 17

looking at our laws. We have 0 and 1. Can you see that?

So we must now set up a NUMBER LINE with 0 and 1 so we can set up our inequalities.
Number line: (Copy this and write it down)
<------0-------1------>

Answer 18

group up the inequalities in the laws for \[|x^2-1|\] and \[|x|\]

Answer 19

oks
and now?

Answer 20

the circle numbers are for the grouping, dont worry to much about that for now. Do you understand so far?

Answer 21

yeah

Answer 22

do you still need help?

Answer 23

i will try here. thanx