Thread: Simple proving the inequalities

|x| ≤ 1 ⇒ |x^2 − x − 2| ≤ 3|x + 1|
im guessing you factor it and cancel out the x+1 then im left with this
|x-2| ≤ 3
What do i do from there?

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Now

by the triangle inequality.

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And since

that means .


Therefore

and thus

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