How do you solve #4 - |3k+1| <2#?

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Answer 1 · 2017-04-26T10:54:00

#k<-1#
#k>1/3#

To make the absolute positive multiply everything by (-1). Note that this turns the inequality sign round the other way. So now we have:

#-4+|3k+1| > -2#

Add 4 to both sides

#|3k+1| >+2#

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There are what I will call 'trigger' values that this condition relates to.

Lets determine these 'trigger' values.

Set #|3k+1|=2# this is the same as #|+-2|=2#

So the 'trigger' values are such that
#3k+1=-2 " "=>" " k= -3/3=-1#
#3k+1=+2" "=>" "k=1/3#

so we have #|"increasingly negative"|>2=> k<-1#

and we have #|"increasingly positive"|>2=>k>1/3#