How do you solve absolute value inequality #-3abs(2x-5)<9#?

1 Answer
Alan P.
Apr 9, 2015

Normally we would consider the two cases #(2x-5)# is negative and #(2x-5)# is positive or zero, separately and evaluate each case for restrictions on the value of #x#.

However, in this case
#(-3)abs(2x-5)<9#
can be re-written as
#abs(2x-5)> -3#
(by dividing both sides by #(-3)# and reversing the inequality)

#abs(2x-5) >=0 >-3#
for all values of #x# (based on the definition of absolute value

so the solution to the given inequality is #x epsilon (-oo,+oo)#

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