Question 30616
I do not understand. Question solve each compound ineqaulity and write the solution set using interval notion. 
0<5-2x<=10 and -6<4-x<0
PLEASE SEE SOURCE FOR GOOD REPRESENTATION ON NUMBER LINE...CLICK 
'SHOW SOURCE'BUTTON TO SEE THE GRAPH OF NUMBER LINE....

{{{drawing(600,600,-10,20,-10,20,red( line( -2.5, 0, 10,0 ) ),locate( -2.5, 0,A-2.5  ),locate( 2.5, 0, B2.5 ),locate( 4, 0, P4 ),locate(10,0,Q10 ))}}}
IN THE ABOVE DIAGRAM X SHOULD BE BETWEEN A AND B AS PER I SET AND SHOULD BE BETWEEN P AND Q AS PER II SET.WE FIND THERE IS NO COMMON GROUND BETWEEN THE TWO.HENCE THERE IS NO SOLUTION.SEE BELOW FOR WORKING.

TAKE ONE BY ONE THE INEQUALITIES.
0<5-2X
2X<5
X<5/2
X<2.5
NOW 5-2X<=10
5-10<=2X
-5<=2X
-5/2<=X
-2.5<=X
SO PLOT THIS ON A NUMBER LINE FOR EASE OF UNDERSTANDING
......-2.5............0...................2.5..............................
........=XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX<...SHOWS THE ZONE WHERE X CAN BE AS PER THIS INEQUALITY..NOW TAKE THE SECOND ONE...
-6<4-X
X-6<4
X<10
4-X<0
4<X....
NOW PLOT THIS ON OR ALONG THE ABOVE NUMBER LINE
......-2.5............0...................2.5...................................
........=XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX<...SHOWS THE ZONE WHERE X CAN BE AS PER I SET
......-2.5............0...................2.5....4...............10...........
..................................................<XXXXXXXXXXXXXX<.....SHOWS THE ZONE WHERE X CAN BE AS PER II SET
WE FIND THERE IS NO COMMON ZONE FOR X SATISFYING BOTH SETS...SO THERE IS NO SOLUTION..