How do you solve the inequality #x+5<abs(x+5)# and write your answer in interval notation?

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Answer 1 · 2017-02-20T03:57:21

#(-oo,-5)#

For #x > =-5#, we have #abs(x+5) = x+5# so there are no solutions greater than or equal to #-5#.

For #x < -5#, we have #x+5 < 0 <= abs(x+5)#

So the solution set is #(-oo,-5)#

Another explanation

If #a# is positive, then #a = absa#

Is #a# is negative, then #a < absa#

#x+5# is negative for #x < -5#