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Question
If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].
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Solution
\[\left| z + 1 \right| = \left| z + 4 - 3 \right|\]
\[ \leq \left| z + 4 \right| + \left| - 3 \right|\]
\[ \leq 3 + 3\]
\[ = 6\]
\[\text { Also }, \]
\[\left| z + 1 \right| \geq 0\]
\[\text { Thus }, 0 \leq \left| z + 1 \right| \leq 6 .\]
Hence, the greatest and least values of
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