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Math Help - inequalities

  1. #1
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    inequalities

    2(x-3)-3(x+2)<5

    i seriously don't know where to start. I was thinking of putting 5 on the other side, but i would be stuck from there.

    P.S. if i do find the numbers for instance, 3,-3, 8. I would have to graph them on a number line and see if its a positive or negative which i know how to do but i am confused on how to figure out the final answer from that
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  2. #2
    Super Member 11rdc11's Avatar
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    2(x-3)-3(x+2)<5

    1) Distribute

    2x-6 -3x-6<6

    2) Combine like terms

    -x<18

    3) Divide by -1 and remember to change your sign

    x>-18
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  3. #3
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    so there is only 1 answer? in the questions my teacher showed us there were mutiply answers like x^2(x-16)(x-3)<=0 and the answer was 3<=x<=16

    and how you get <6 when it was <5?
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  4. #4
    Super Member 11rdc11's Avatar
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    The amount of answers depend on the degree of the exponent. So in this case it was to the degree of 1 so you had 1 answer. Now x^2 is to the degree of 2 so you will have at most 2 solutions
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