(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show the following for every d>0:

For every real number x with |x-1|<d it follows that |1+x|<2+d

2. The attempt at a solution

If x-1>0, then |x-1|=x-1<d. Hence x+2 = |x+2| < 2+d.

If x-1<0, then |x-1|=-(x-1)<d. Hence x-1>-d => x+1 > 2-d ...??

Is this really possible to do without putting any other restrictions on d?

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# Homework Help: Absolute value

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