Question

If x<−7 then |4−|3+x|| equivalent to...
a.|1+x|
b.|1−x|
c.−x−7
d.|x−7|
e.x+7

Answer 1

If x<-7 then |x+3|=-x-3 so |4-|3+x||=|4+x+3|=|x+7| when x<-7 |x+7|=-x-7 so the answer is c

Answer 2

why?

Answer 3

Err do you know defintion of |x| function?

Answer 4

yes..i know but i don't understand here

Answer 5

Ok so
f(x)=|x| is defined as f(x) = x,x>0 -x,x<0
Now replace x by x-3
f(x)=|x-3| is defined as x-3,x-3>0, -(x-3), x-3<0,
do you get that?

Answer 6

yeah..I got it

Answer 7

so in your querstion first simply the inner mod |x+3| is -(x+3) when x+3<0 or x<-3 (x<-7 is included here) so you get that -x-3 so the outer mod becmes |x+7| which is -x-7. Did you understand?

Answer 8

yes i'm understand

Answer 9

If your're still confused say so....

Answer 10

ok..thanks before