What is the solution set for #abs(4x – 3) – 2 > 3#?

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Answer 1 · 2018-03-23T11:09:56

#(-oo,-1/2)uu(2,oo)#

If we look at the definition of absolute value:

#|a|=a \ \ \ \ \ \ \ \ # if and only if # \ \ \ a>=0#

#|a|=-a \ \ \ # if and only if # \ \ \ a<0#

It follows from this, that we need to solve both:

#4x-3-2>3# and #-(4x-3)-2>3#

#4x-3-2>3#

#4x-5>3#

#x>8/4#

#color(blue)(x>2)#

#-(4x-3)-2>3#

#-4x+3-2>3#

#-4x>2#

#color(blue)(x<-1/2)#

This gives us a union of intervals:

#(-oo,-1/2)uu(2,oo)#