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## Homework Statement

Prove that -1< x < 0 implies |x^2 - 2x +1| < 1.25|x-1|

## The Attempt at a Solution

Attempt at 1st question:

|(x-1)(x^2 + x -1)| < 1.25|x-1|

|(x^2 + x -1)| < 1.25

-1.25 < (x^2 + x -1) < 1.25

-0.25 < x^2 + x < 2.25

-0.5 < (x + 0.5)^2 < 2.25 **

this leads to

0 < (x + 0.5)^2 < 2.25

0 < x + 0.5 < 1.5 **

0 < x < 1

0 > x > -1

I don't have the answers to this in my book, but does this rough work for the proof look ok?

*edit: I just realized that this is completely wrong, that I didn't add correctly on the steps marked by **

## Homework Statement

Prove that -3 <= x <= 2 implies |x^2 + x - 6| <= 6|x-2|

## The Attempt at a Solution

Attempt at 2nd question:

|(x+3)(x-2)| <= 6|x-2|

|x+3| <= 6

-6 <= x + 3 <= 6

-9 <= x <= 3

how does this imply -3 <= x <= 2?? Not sure how to do this one.

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