Question 159
Determine the real numbers $a$, $b$, $c$ and $d$ for which the inequality
$$
|x+a| + |y+b| + |z+c| + |x+y+z+d| \geq |x| + |y| + |z| + |x+y+z|
$$
holds for any real numbers $x$, $y$ and $z$.
$$
|x+a| + |y+b| + |z+c| + |x+y+z+d| \geq |x| + |y| + |z| + |x+y+z|
$$
holds for any real numbers $x$, $y$ and $z$.