Question 1
Prove that for all real $x$ and $y$ the inequality
$$
|x + y| + |x + 1| + |y + 1| \geq 2
$$
holds. For what $x$ does there exist $y$ such that $|x+y|+|x+1|+|y+1| = 2$?
$$
|x + y| + |x + 1| + |y + 1| \geq 2
$$
holds. For what $x$ does there exist $y$ such that $|x+y|+|x+1|+|y+1| = 2$?