G2.3 Determine the sum of all real roots of the following equation $|x+3|-|x-1|=x+1$.
When $x \leq-3$, the equation becomes $-x-3-(1-x)=x+1 \Rightarrow x=-5$
When $-3<x \leq 1$, the equation becomes $x+3-(1-x)=x+1 \Rightarrow x=-1$
When $1<x$, the equation becomes $x+3-(x-1)=x+1 \Rightarrow x=3$
$\therefore$ Sum of all real roots $=-5+(-1)+3=-3$
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