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If |z+4|lt=3 then find the greatest and ...

If `|z+4|lt=3` then find the greatest and least values of `|z+1|dot`

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`|z+4| leq 3 Rightarrow-3 leq z+4 leq 3 `

`Rightarrow-6 leq z+1 leq 0 `

`Rightarrow 0 leq-(z+1) leq 6 `

`Rightarrow 0 leq|z+1| leq 6`

The greatest and least values are `6` and` 0` .

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