MHB How can you rewrite expressions using the definition of absolute value?

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The definition of absolute value indicates that |x| equals x for non-negative values and -x for negative values. An example provided is the expression |-sqrt{3} - sqrt{5}|, which is negative. By applying the definition, this expression can be rewritten as -(-sqrt{3} - sqrt{5}), resulting in sqrt{3} + sqrt{5}. This confirms the correct application of the absolute value definition in rewriting expressions.
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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.

| -sqrt{3} - sqrt{5} |

Since the expression in the absolute value is less than 0, we can say -(-sqrt{3} - sqrt{5}), which becomes
sqrt{3} + sqrt{5}.

Correct?
 
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Yes, that is correct.
 

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