Question

If 6<|x-3|<7 and x<0 find the value of |x|

Answer 1

don't you hate these?

Answer 2

a smidge.

Answer 3

especially when you have to start proving things with them.

Answer 4

haha that is the best part...NOT!

Answer 5

-7<x-3<-6
-4<x<-3

Answer 6

oh it wants the abs value.....
3<|x|<4

Answer 7

ok lets see.
\[6<|x-3|\] gives
\[6<x-3\] or
\[x-3<-6\] first ones says
\[3<x\] so we throw it out
second one says
\[x<-3\] so that is possible

Answer 8

haha that is the best part...NOT!

Answer 9

joemath is right !

Answer 10

second one says
\[|x-3|<7\] means
\[-7<x-3<7\]
\[-4<x<10\]

Answer 11

so we know that
\[x<0\]
\[x<-3\]
\[x>-4\] making the interval
\[(-4,-3)\] unless my algebra is bad

Answer 12

thats right.

Answer 13

well not nearly as snappy as your way

Answer 14

but more thorough . and definitely appreciated!

Answer 15

guess thinking is better. since
\[x<0\] we know
\[|x-3|=3-x\]

Answer 16

so put
\[6<3-x<7\]
\[3<-x<4\]
\[-4>x>-3\] easy

Answer 17

12?