[tex] \it |x+2| +m=1 \Rightarrow |x+2| = 1 -m \Rightarrow x+2 = \pm(1-m)
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I)\ x+2 = -(1-m) \Rightarrow x+2= -1+m \Rightarrow x= -1+m-2 \Rightarrow
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x = m-3 < 1 \Rightarrow m<4 \ \ \ \ \ (1)
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II)\ \ x+2 = 1-m \Rightarrow x = 1-m-2 \Rightarrow x = -m-1 <1 \Rightarrow
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\Rightarrow -m<2|_{\cdot(-1)} \Rightarrow m>-2 \ \ \ \ \ (2) [/tex]
[tex] \it (1), (2) \Rightarrow m \in(-2,\ 4) [/tex]