11.31 $|x+1|>2|x+2|$.

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11.31 $|x+1|>2|x+2|$.
11.31 We have $|x+1|=0$ when $x=-1$, and $|x+2|=0$ when $x=-2$. We will solve the given inequality in the intervals $(-\infty,-2)$, $[-2,-1)$, and $[-1, \infty)$.

1) If $x-2 x-4$, then $x>-3$. Therefore, $-32 x+4$, or $3 x2 x+4$, from which $x<-3$. In this case, there are no solutions.

Combining the solutions (1) and (2), we get that $-3<x<-\frac{5}{3}$. Answer: $\left(-3,-\frac{5}{3}\right)$