How do you solve the inequality: #abs(x - 8) < 5#?

Answer 1

#3 < x < 13#

In order to solve this absolute value inequality, you need totake into account the two possible signs the expression inside the modulus can have

The inequality will become

#x - 8 < 5#
#x < 13#

This time, the inequality will be

#-(x-8) < 5#
#-x + 8 < 5#
#x > 3#
So, the solution set for this inequality will include any value of #x# that is bigger than #3# and smaller than #13#.
This means that you have #3 < x < 13#, or #x in (3, 13)#.
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Answer 2

To solve the inequality |x - 8| < 5, you set up two separate inequalities:

  1. x - 8 < 5
  2. -(x - 8) < 5

Then, solve each one separately:

  1. x - 8 < 5 Add 8 to both sides: x < 13

  2. -(x - 8) < 5 Distribute the negative sign: -x + 8 < 5 Subtract 8 from both sides: -x < -3 Multiply both sides by -1 (to maintain the inequality direction): x > 3

So, the solution is 3 < x < 13.

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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.

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.

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.

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.

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