SOLUTION: 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

Algebra ->  Inequalities -> SOLUTION: 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      Log On


   

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
Found 2 solutions by Nate, venugopalramana:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
0<5-2x<=10
0<5-2x
-5<-2x
(5/2)>x
interval notation: [-5/2, +infinity)
and
5-2x<=10
-2x<=5
x>=(-5/2)
interval notation: (-infinity, 5/2)
-------------------------------------------------------------------------------
-6<4-x<0
-6<4-x
-10<-x
10>x
interval notation: (-infinity, 10)
and
4-x<0
-x<-4
x>4
interval notation: (4, +infinity)

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
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....

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 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...........
.................................................. WE FIND THERE IS NO COMMON ZONE FOR X SATISFYING BOTH SETS...SO THERE IS NO SOLUTION..