How do you solve #6| y + 4| + 8> - 40#?

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Answer 1 · 2017-07-22T13:37:31

#y<4 or y> -12#

#6abs(y+4)+8 > -40#
#6abs(y+4) > -48#
#abs(y+4) > -8#

We know that #abs(5)=(5)=5 #,where#5>0 #
#abs(-5)=-(-5)=5#,where #-5<0#

So,#abs(x)#, if #x>0#, then #abs(x)=x#
if #x<0#, then#abs(x)=-(x)#
You get the point.

We don't know whether #(y+4)# is positive or negative.
So we will break it into two cases.

Case1: #(y+4)>0#
Then,#y+4> -8#
#y> -12#

#OR#

Case 2: #(y+4)< 0#
Then, #-y-4> -8#
#y<4#

So, the answer is #y<4 or y> -12#