MHB How do I rewrite expressions using absolute value?

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The absolute value definition states that |x| equals x for non-negative x and -x for negative x. An example provided involves rewriting the expression |1 - sqrt{2}| + 1. Since 1 - sqrt{2} is negative, it is rewritten as -(1 - sqrt{2}) + 1. This simplifies to -1 + sqrt{2} + 1, resulting in sqrt{2}. The final answer is confirmed as correct.
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The definition of absolute value states the following:

| x | = x when x is > or = 0

| x | = -x when x < 0

I can use the above definition to rewrite expressions that do not contain absolute values.

| 1 - sqrt{2} | + 1

The value 1 - sqrt{2} is less than 0.

So, we have -(1 - sqrt{2}) + 1.

-1 + sqrt{2} + 1

Answer: sqrt{2}

Correct?
 
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Yes, this is correct.
 

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