How do you solve the inequality #abs(3-x)>=x-5# and write your answer in interval notation?

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Answer 1 · 2017-03-21T17:44:23

See below.
The inequality is true #forall x in RR#

We have #abs(x-3) ge x-3-2# Now supposing #x ne 3# we can do

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

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

or

#1+2/abs(x-3) ge pm 1#

or

#1 le 2/abs(x-3)+1#

or

#abs(x-3) le 2 + abs(x-3)#

or

#2 ge 0# which is true for all #x#