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24-06-2022
Mathematics

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Rewrite each of the following expressions without using absolute value: |x-5|+|x+5| if x<-5

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konrad509 konrad509

24-06-2022

For [tex]x < -5[/tex]:

[tex]x-5 < 0 \Rightarrow |x-5|=-(x-5)=-x+5\\x+5 < 0\Rightarrow |x+5|=-(x+5)=-x-5[/tex]

So

[tex]|x-5|+|x+5|=-x+5-x-5=-2x[/tex]

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