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Inequalities

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    I have the inequality:
    -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\leq15
    I then divided the first sub-inequality (SI 1) by 2:
    (SI 1) -10<2x
    (SI 1) -5<x
    I then divided the second sub-inequality (SI 2) by 2:
    (SI 2) 2x\leq15
    (SI 2) x\leq7.5
    Through combining SI 1 and SI 2 I form the following:
    -5<x\leq7.5

    Here comes the easiest part of all, but somehow the hardest at the moment for me. 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.
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    7.5 would be in there if it were an integer

    but the most your x can be is 7.5, so how could it b 8?
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    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
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    THANKS a LOT !

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Updated: April 10, 2012
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