-17 < x < 12 and 12 < x < 24

Make the number line graph of -17 < x < 12 


-----o=====================o---------o-----
   -17                    12        24

Make the graph of 12 < x < 24 on another number line
using the same scale as the first:

-----o---------------------o=========o-----
   -17                    12        24 

Place them one above the other:

-----o=====================o---------o-----
   -17                    12        24
-----o---------------------o=========o-----
   -17                    12        24

Since the word between the inequalities is "AND",
We must make a single number line of what points
are shaded on on BOTH number lines.

But as you can see there is no interval that is
shaded on the first number line AND shaded on the 
second number line, so the solution set is the empty
set which is written ∅.

Edwin