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If $|z+4| \leq 3$, then the greatest and the least value of $|z+1|$ are
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Verified Answer
The correct answer is:
6,0
$|z+4| \leq 3 \Rightarrow-3 \leq z+4 \leq 3$
$\begin{array}{l}
\Rightarrow-6 \leq \mathrm{z}+1 \leq 0 \\
\Rightarrow 0 \leq-(\mathrm{z}+1) \leq 6 \\
\Rightarrow 0 \leq|\mathrm{z}+1| \leq 6
\end{array}$
Hence, the greatest and least values are 6 and 0.
$\begin{array}{l}
\Rightarrow-6 \leq \mathrm{z}+1 \leq 0 \\
\Rightarrow 0 \leq-(\mathrm{z}+1) \leq 6 \\
\Rightarrow 0 \leq|\mathrm{z}+1| \leq 6
\end{array}$
Hence, the greatest and least values are 6 and 0.
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