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Inequalities

I have the inequality:
−2<2x5≤3-2<\frac{2x}{5}\leq3
I have to find all the possible integer values of x in the inequality above.
First I multiplied both sides by 5 to get:
−10<2x≤15-10<2x\leq15
I then divided the first sub-inequality (SI 1) by 2:
(SI 1) −10<2x-10<2x
(SI 1) −5<x-5<x
I then divided the second sub-inequality (SI 2) by 2:
(SI 2) 2x≤152x\leq15
(SI 2) x≤7.5x\leq7.5
Through combining SI 1 and SI 2 I form the following:
−5<x≤7.5-5<x\leq7.5

Here comes the easiest part of all, but somehow the hardest at the moment for me:s-smilie:. I now have to find all the possible integer values of x. I easily understand that -5 will NOT be included as a possible integer because of the sign next to it. However the 7.5 part with the sign confuses me. :confused:

Is 8 included or not? WHY?
Or do I just have the possible integers to be:
-4,-3,-2,-1,0,1,2,3,4,5,6 and 7 ?

Whether 8 gets included or not, please explain to me why.
Thanks a lot.
Reply 1
Avatar for TenOfThem
TenOfThem
18
7.5 would be in there if it were an integer :biggrin:

but the most your x can be is 7.5, so how could it b 8?
Reply 2
Avatar for signwithme
signwithme
7
the inequality sign is less than or equal to so everything up to and including 7.5 is a value of x but nothing about that so 8 wouldnt be
Reply 3
Avatar for krisshP
krisshP
OP
14
THANKS a LOT ! :smile::smile::smile::smile::smile::smile::smile::biggrin:

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