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?
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?
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?