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

If |x-1| < 1 then Prove |x^2 -4x + 3| < 3.

2. Relevant equations

3. The attempt at a solution

proof: Assume |x-1| < 1. Then X has to be between 0 and 2.Because X has to be between 0 and 2 then |x-3|<3,and |x-1||x-3|<3 by multiplication of inequalities.

|x-1||x-3|=|x^2 - 4x + 3| by distribution. Thus, |x^2 -4x + 3| < 3. (QED)

I was wondering if this is sufficient. I was a little unsure if what I did in the second sentence, and the start of the third was ok

Thank you.

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# Homework Help: Inequality Proof

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