Treat as two inequalities: -11<3-x; 3-x<11. So add x to both sides of the first inequality: x-11<3; add 11 to each side: x<14.
Now the second inequality. Add x to both sides: 3<11+x and subtract 11 from both sides: -8<x, so x>-8.
Now we can rewrite this as x lies between -8 and 14: -8<x<14.
Check: pick a value of x in the range. Let's pick x=0 and plug into the original statement:
-11<3<11 is true. Now plug in a value outside the range. Let's pick x =15 and plug it in: -11<-12<11. Only half true, so it's false. Pick x=-10 and plug in: -11<13<11. Only half true, so it's false.