SOLUTION: |x-4|=5, I am the parent of a teen, and am TOTALLY lost on how to do this, please explain in simple english, he is supposed to have a positive and a negative answer.

Algebra ->  Algebra  -> Absolute-value -> SOLUTION: |x-4|=5, I am the parent of a teen, and am TOTALLY lost on how to do this, please explain in simple english, he is supposed to have a positive and a negative answer.       Log On

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Question 25375: |x-4|=5, I am the parent of a teen, and am TOTALLY lost on how to do this, please explain in simple english, he is supposed to have a positive and a negative answer.
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
Whenever you have an absolute value equal to a positive number, there will be TWO solution.

As an easy example, consider abs%28x%29+=+5. The two solutions will be
x=5 and x= -5.

Likewise, consider abs%28y%29+=+5. The two solutions will be
y=5 and y = -5.

Now, consider abs%28x-4%29+=+5. The two solutions will be
x-4=5 and x-4=-5.

So, here we go:
+abs+%28x-4%29+=+5

There are two solutions:

First Solution:
x-4 = 5
x-4 +4 = 5+4
x = 9

Second Solution:
x-4 = -5
x-4 +4 = -5 +4
x=-1

Check: x=9
| x-4 | = 5
|9-4| = 5
5=5

Check: x=-1
| x-4 | = 5
|-1-4| = 5
5=5

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