Question

x|x|<=|x-2|

Answer 1

is that a left arrow, or you meant ≤ ?

Answer 2

yes

Answer 3

please help me

Answer 4

what does the absolute value mean?

Answer 5

if we have - in the absolute it same as +
please find the x value. sorry my english is not good

Answer 6

first try to draw graph of \[x\left| x \right|\]

Answer 7

x value ?

Answer 8

graph the function \[y=x \left| x \right|\]

Answer 9

ok i'll help. what would x|x| equal to when x>0?

Answer 10

ya

Answer 11

it will equal to\[x^2\]

Answer 12

do you understend why?

Answer 13

ya cause there absolute value, right? next how?

Answer 14

now what x|x| be when x<0?

Answer 15

be +

Answer 16

try some negative numbers -3 for example: (-3)|-3|=(-3)*3=-3^2

Answer 17

now lets generalize when x is negative (or x<0) x|x|=-x^2

Answer 18

do you understand this?

Answer 19

no
i need the value of x

Answer 20

what part don't you understend?

Answer 21

i can explain in english, my english is not good

Answer 22

ok lets start again :D

Answer 23

first lets graph the function y=x|x|

Answer 24

it has too cases when x>0 and when x<0

Answer 25

first try when x>0 (or positive) for example 4:
4|4|=4*4=4^2, now lets generalize when x>0 x|x|=x^2

Answer 26

do you understand so far?

Answer 27

yes

Answer 28

ok now lets try x<0 (or negative) for example -3:
(-3)|-3|=-3*3=-3^2, now lets generaliza when x<o x|x|=-x^2

Answer 29

do you understand this?

Answer 30

no. how fool i'm

Answer 31

no you aren't fool!

Answer 32

you have x|x| right so when you substitute negative number for x you get (negative)*(positive)=(negative) because only one x is in absolute value and it makes one term positive and one negative

Answer 33

dose it make more sence now?

Answer 34

yes, thank you leon :)

Answer 35

ok now lets use our knowlidge to graph y=x|x|

Answer 36

as we shown when x>0 y=x^2

Answer 37

i drow only positive halfe of parabola y=x^2, because we are just talking about x>0

Answer 38

do you understend this?