If $|z+4| \leq 3$, then find the greatest and least values of $|z+1|$.
$|z+1|=|z+4-3|$
$\leq|z+4|+|-3|$
$\leq 3+3$
$=6$
Also,
$|z+1| \geq 0$
Thus, $0 \leq|z+1| \leq 6$.
Hence, the greatest and least values of $|z+1|$ is 6 and 0 .
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