# Math Help - Simple proving the inequalities

1. ## 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?

2. $|x - 2| = |x + (-2)|$.

Now

$|x + (-2)| \leq |x| + |(-2)|$ by the triangle inequality.

$|x + (-2)| \leq |x| + 2$.

And since $|x| \leq 1$

that means $|x| + 2 \leq 3$.

Therefore $|x - 2| \leq 3$

and thus

$|x| \leq 1 \implies |x^2 - x - 2| \leq 3|x + 1|$.