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

Answer 1

Eva Adamson

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

Taking a look at how absolute value is defined:

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

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

This means that we must resolve both of them:

#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)#

We are then left with a union of intervals:

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

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Answer 2

Jace Anderson

The solution set for |4x - 3| - 2 > 3 is x < 1/2 or x > 5/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

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