How do you solve the inequality #x+abs(2x-3)<2# and write your answer in interval notation?

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Answer 1 · 2017-03-22T19:57:50

The inequality is not observed for any #x in RR#

Consider

#abs(2x-3) < 2-x# Supposing #x ne 2# we have

#abs(2x-3)/abs(2-x) < (2-x)/abs(2-x)# or

#abs(2x-3)/abs(2-x) < pm 1#

or

#abs(2x-3)/abs(2-x) < min(-1, 1) = -1#

arriving at

#abs(2x-3)/abs(2-x) < -1# which is impossible so does not exist any value for #x# making feasible this inequality.