How do you solve #|-6x + 3| ≥ 39#?

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Answer 1 · 2017-01-17T04:37:55

#|-6x+3|>=39 <=> x in (-oo,-6]cup[7,oo)#

#(|x|=x <=> x>=0) and (|x|=(-x) <=> x<0)#

So, if #(-6x+3)<0# then #|-6x+3|=6x-3#

Then,

#6x-3>=39#

#<=>#

#6x>=42#

#<=>#

#x>=7#

Or, if #(-6x+3)>=0# then #-6x+3>=39#

#<=>#

#-6x>=36#

#<=>#

#x<=-6#

Then #x<=-6# or #x>=7#

#<=># #x in (-oo,-6] cup [7,oo) #