How do you solve the inequality #|2x+3| > |x- 4|#?

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Answer 1 · 2017-02-26T00:11:04

#x < -7# or #x > 1/3#

#|2x+3| > |x- 4|# supposing #x ne 4# we have

#abs((2x+3)/(x-4)) > 1# or equivalently

#-1 < (2x+3)/(x-4) < 1# or

#-x+4 < 2x + 3->x > 1/3#

or

#2x+3 < x-4->x < -7#

The feasible #x# are:

#x < -7# or #x > 1/3#