How do you solve the absolute value inequality and express the solution set in interval notation for #-2abs(s-3)<-4#?

1 Answer
Alan P.
Apr 10, 2015

Multiplying both sides of an inequality by a negative value reverses the inequality
So
#-2abs(s-3) < -4#
is equivalent to
#abs(s-3) > 2#

If #(s-3)# is negative (i.e. #s<3#)
then this becomes
#3-s > 2#
#-s>-1#
#s<1#

If #(s-3)# is positive or zero (i.e. #s>=3#)
then
#(s-3)>2#
#s>5#

So
#s epsilon (-oo,1)uuu(5,+oo)#

Related questions
See all questions in Absolute Value Inequalities
Impact of this question
4119 views around the world
You can reuse this answer
Creative Commons License