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Math Help - I'm unsure of some problems

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    16

    I'm unsure of some problems

    these are problems that can either be answered with a decimal or fraction, but the book only provides the fraction answer and i do decimal methods, so im worried i may have done something wrong...
    numbers written like this: 1/2, 4/5
    15. -2/3(6 - 2a)=6
    multiply by -3/2
    6-2a=-9
    -6 from each side
    -2a=-15
    divide each side by -2
    a=7.5
    the book says the answer is 15/2
    18.16=5(1-x)
    distribute 5...
    16=5-5x
    -5 from each side..
    11=-5x
    divide each side by -5
    -2.2=x
    the book doesnt give an answer, so i'm even more worried about its correctness, lol.
    20.n-4(1+5n)=-2
    distribute -4...
    n-4-20n=-2
    add 4 to each side
    n-20n=2
    1n-20n=-19n
    -19n=2
    divide each side by -19
    n=-0.105263158
    book doesnt provide an answer, and the sheer length of the decimal has me worried, lol
    and finally,
    22.6m-3=10-6(2-m)
    10-6=4
    distribute 4
    6m-3=8-4m
    add 4m to each side
    10m-3=8
    add 3 to each side
    10m=11
    divide each side by 10...
    m=1.1
    the main thing im worried about here is that the teacher said between problem 17 and 22 there was 1 problem with 'all numbers' as an answer and 1 problem with 'no solutions' as an answer. i got the all numbers one, but the answers to all the others, unless i did something wrong, are
    17. -2=z
    18. 2=h
    19. all numbers
    20. r=-5
    21. x=-15
    22. m=1.1
    so, 22 seems the most likely to have been the one i made a mistake in, due to the fact all the others have solid non-decimal answers.
    thanks in advance
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    these are problems that can either be answered with a decimal or fraction, but the book only provides the fraction answer and i do decimal methods, so im worried i may have done something wrong...
    numbers written like this: 1/2, 4/5
    15. -2/3(6 - 2a)=6
    multiply by -3/2
    6-2a=-9
    -6 from each side
    -2a=-15
    divide each side by -2
    a=7.5
    the book says the answer is 15/2 -----Okay. But what is 15/2? Is it 7.5?

    ---------------------------------
    18.16=5(1-x)
    distribute 5...
    16=5-5x
    -5 from each side..
    11=-5x
    divide each side by -5
    -2.2=x
    the book doesnt give an answer, so i'm even more worried about its correctness, lol.

    One good way to check if your answer is correct is to plug/substitute your answer into the original equation. If your answer proves the equation true, then you have the correct amswer--even if the book's answer says otherwise. If your answer shows the original equation is false, then your answer is wrong.

    So, here, your answer is x = -2.2. Substitute that into
    16 = 5(1-x),
    16 =? 5(1 -(-2.2))
    16 =? 5(1 +2.2)
    16 = 5(3.2)
    16 =? 16
    Yes, so, OK, your x = -2.2 is correct.


    ---------------------------
    20.n-4(1+5n)=-2
    distribute -4...
    n-4-20n=-2
    add 4 to each side
    n-20n=2
    1n-20n=-19n
    -19n=2
    divide each side by -19
    n=-0.105263158
    book doesnt provide an answer, and the sheer length of the decimal has me worried, lol

    Why not just n = -2/19 then?
    After -19n = 2,
    n = 2/(-19)
    n = -2/19.

    Check that by substituting it into the original equation. (It is correct, I checked.)


    -----------------------------
    and finally,
    22.6m-3=10-6(2-m)
    10-6=4 ----------------------this not correct. The -6 is connected to the (2-m). You cannot treat the -6 as separate.
    Here is the continuation,
    distribute -6,
    6m -3 = 10 -12 +6m
    subtract 6m from each side,
    -3 = -2
    Whoa, no more unknown?
    Besides, -3 is not equal to -2 either.
    So, the given equation has no solution.


    6m-3=8-4m
    add 4m to each side
    10m-3=8
    add 3 to each side
    10m=11
    divide each side by 10...
    m=1.1
    the main thing im worried about here is that the teacher said between problem 17 and 22 there was 1 problem with 'all numbers' as an answer and 1 problem with 'no solutions' as an answer. i got the all numbers one, but the answers to all the others, unless i did something wrong, are
    17. -2=z
    18. 2=h
    19. all numbers
    20. r=-5
    21. x=-15
    22. m=1.1
    so, 22 seems the most likely to have been the one i made a mistake in, due to the fact all the others have solid non-decimal answers.
    thanks in advance.
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