hi guys,
how do you solve this inequality ?
|x| + |x-1| < 5
thank you
You probably need to use the Triangle Inequality.
$\displaystyle \displaystyle |a + b| \leq |a| + |b|$.
So that means $\displaystyle \displaystyle |x + x - 1| \leq |x| + |x - 1|$
$\displaystyle \displaystyle |2x - 1| \leq |x| + |x - 1|$.
And since $\displaystyle \displaystyle |x| + |x - 1| < 5$ that means
$\displaystyle \displaystyle |2x - 1| < 5$.
Can you go from here?