Question 736712: Michel writes the expression |x - 5|,
where x is a real number, without the
absolute value symbol. His answer is
shown below.
|x - 5| = {x - 5, if x - 5 ≥ 0
-(x - 5), if x - 5 < 0
|x - 5| = {x - 5, if x ≥ 5
5 - x, if x < 5
explain the steps in Michel's solutions
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! -------
Michel writes the expression |x - 5|,
where x is a real number, without the
absolute value symbol. His answer is
shown below.
|x - 5| = {x - 5, if x - 5 an ≥ 0
-(x - 5), if x - 5 < 0
|x - 5| = {x - 5, if x ≥ 5
5 - x, if x < 5
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Since "x" is a variable we cannot tell whether x-5
is negative or not negative.
----
Michael has considered both of the possible conditions
and followed the definition of
|x| = x if x >= 0
or -x if x < 0
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Cheers,
Stan H.
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