SOLUTION: Here is the problem: The solution set of which of the following equations is the set of real numbers that are 5 units from -3? I know that it ends up being |x+3|=5. However,

Question 637657: Here is the problem:
The solution set of which of the following equations is the set of real numbers that are 5 units from -3?
I know that it ends up being |x+3|=5. However, why does the negative 3 become +3 in the equation?
Thank you.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

The absolute-value notation is bars, not parentheses or brackets.
Use the proper notation; the other notations do not mean the same thing.
It is important to note that the absolute value bars do NOT work in the same way as do parentheses.
Whereas �(�3) = +3, this is NOT how it works for absolute value:
Simplify �| �3 |.
Given �| �3 |, I first handle the absolute value part, taking the positive and converting the absolute value bars to parentheses:
�| �3 | = �(+3)
Now I can take the negative through the parentheses:
�| �3 | = �(3) = �3
As this illustrates, if you take the negative of an absolute value, you will get a negative number for your answer.
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