1. Multiple absolute value inequality

Hello, I was asked to solve this inequality analytically.

|x^2 - x| - |x| < 1

However, I do not know how to start it....
I'm not sure how to solve inequalities with more than one
absolute value in it. How would I solve this?

2. You use the what's called known as triangle inequalities:

$\displaystyle |a+b|\le|a|+|b|$

$\displaystyle |a|-|b|\le |a-b|$

$\displaystyle | |a| +|b| |\le |a-b|$

So you can do:

$\displaystyle |x^2-x|-|x| \le |x^2-x -x|$

which:

$\displaystyle |x^2-x-x|=|x^2-2x|$

so your last line would be:

$\displaystyle |x^2-2x|<1$

Are you supposed to solve for x?

3. I guess I am supposed to find the intervals of x which satisfies the inequality. Thank you for your help, it's looking good so far. I hadn't learned about the triangle inequalities before.

4. no problem, so you can take it from there? if you run into any more trouble i'm glad to help

5. I'll give it a try for now. Thank you for the help, I'll see if i run into any problems.