How do you solve #|3x - 3| < 4#?

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Answer 1 · 2016-11-05T05:28:10

#x# lies between #-1/3# and #7/3#
or #-1/3 < x < 7/3#
or #(-1//3,7/3)#

#|3x-3|<4# means

either #3x-3<4# i.e. #3x<4+3# ot #3x<7# or #x<7/3#

or #-(3x-3)<4# i.e. #-3x+3<4# or #-3x<4-3#

or #-3x<1# or #x> -1/3#

This means #x# lies between #-1/3# and #7/3#

We can combine the two statements #x<7/3# and #x> -1/3#

together as #-1/3 < x < 7/3# or in interval form as #(-1//3,7/3)#