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Math Help - Simplifiying - problem with parentheses

  1. #1
    b47
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    Simplifiying - problem with parentheses

    I'm trying to teach myself how to simplify expressions and I'm having trouble with these two:

    1. x - 2(9 + 6x)
    2. 2(x - y)

    I have been told that the answers are:
    1. -11x -18
    2. 2x - 2y
    ... but I have no idea how to get those answers.

    This is how I tried to simplify them:
    1. x - 2(9) + x - 2(6x)
    2. 2(x) + 2(-y)

    I think that is not right, but I don't understand what I'm doing wrong. How do you simplify these?

    Thanks for any help.
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  2. #2
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    Quote Originally Posted by b47 View Post
    I'm trying to teach myself how to simplify expressions and I'm having trouble with these two:

    1. x - 2(9 + 6x)
    2. 2(x - y)

    ...
    to #1.:

    To be exact your term has to be written like this:

    x-2*(9+6x)

    If you multiply a sum (written in brackets) you must multply each summand by the leading factor:

    x-2*(9+6x) = x-2*9 - 2*(6x)

    You have to observe the sign rules when multiplying: If the signs of the factors are equal (+*+ or -*-) the the result is positive (+) else it is negative.
    Since 9 and 6 (of 6x) are positive numbers the result becomes:

    x-2*9 - 2*(6x) = x-18-12x

    You only can collect like terms, in this case you can collect the xes:

    x-18-12x=-11x-18

    And now it's your turn to do the 2nd example.
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