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What is the solution set for #absx - 1 < 4#?

Answer 1

#-5 < x < 5#

To solve this absolute value inequality, first isolate the modulus on one side by adding #1# to both sides of the inequality

#|x| - color(red)(cancel(color(black)(1))) + color(red)(cancel(color(black)(1))) < 4 + 1#

#|x| < 5#

Now, depending on the possible sign of #x#, you have two possiblities to account for

This means that the inequality becomes

#x < 5#

This time, you have

#-x < 5 implies x> -5#

These two conditions will determine the solution set for the absolute value inequality. Since the inequality holds true for #x> -5#, any value of #x# that's smaller than that will be excluded.

LIkewise, since #x<5#, any value of #x# greater than #5# will also be excluded. This means that the solution set to this inequality will be #-5 < x < 5#, or #x in (-5, 5)#.

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Answer 2

Ethan Adkins

The solution set for |x| - 1 < 4 is -3 < x < 3.

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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 #absx - 1 &lt; 4#?

What is the solution set for #absx - 1 < 4#?