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Math Help - Formula Question

  1. #1
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    Formula Question

    Alright so I have two equations that the paper is giving me to simplify, only problem is I don't know where to start.. and my text book isn't being helpful, so I was wondering if anyone could point me in the right direction? x.x

    2/3 (12t - 18) + 2t - 30

    40 ( 3/8 * Y - 1/4) + 40 (4/5)

    It is also asking me to solve for questions.

    2 - (4x + 7) = 3 + 2 (x + 2) ------ I started solving this one by using distributive property after adding 3+2=5 on the right side, making (x + 2) into 5x + 10..?

    x/3 + x/4 = -2 ------ This one I started by getting the least common denominator of 3 and 4, which made the equation 4x/12 + 3x/12 = 7x/12 ------ From there it left me with 7x/12 = -2 and from there I am stuck.
    Last edited by Uriah5356; March 11th 2009 at 08:13 PM. Reason: Added
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  2. #2
    Member sinewave85's Avatar
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    Quote Originally Posted by Uriah5356 View Post
    Alright so I have two equations that the paper is giving me to simplify, only problem is I don't know where to start.. and my text book isn't being helpful, so I was wondering if anyone could point me in the right direction? x.x

    2/3 (12t - 18) + 2t - 30

    40 ( 3/8 * Y - 1/4) + 40 (4/5)
    First you need to multiply throught the parentheses:

    \frac{2}{3}(12t - 18) +2t -30 = \left(\frac{2}{3}\right)(12t) - \left(\frac{2}{3}\right)(18) + 2t - 30 = 8t -12 +2t - 30

    Then you can just add like terms:

    8t -12 +2t - 30 = 10t -42
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  3. #3
    Member sinewave85's Avatar
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    Quote Originally Posted by Uriah5356 View Post
    Alright so I have two equations that the paper is giving me to simplify, only problem is I don't know where to start.. and my text book isn't being helpful, so I was wondering if anyone could point me in the right direction? x.x

    2/3 (12t - 18) + 2t - 30

    40 ( 3/8 * Y - 1/4) + 40 (4/5)

    It is also asking me to solve for questions.

    2 - (4x + 7) = 3 + 2 (x + 2) ------ I started solving this one by using distributive property after adding 3+2=5 on the right side, making (x + 2) into 5x + 10..?

    x/3 + x/4 = -2 ------ This one I started by getting the least common denominator of 3 and 4, which made the equation 4x/12 + 3x/12 = 7x/12 ------ From there it left me with 7x/12 = -2 and from there I am stuck.

    Where did you get a variable named x from?
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  4. #4
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    Quote Originally Posted by sinewave85 View Post
    Where did you get a variable named x from?
    For which question, those are two individual questions.
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  5. #5
    Member sinewave85's Avatar
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    Quote Originally Posted by sinewave85 View Post
    First you need to multiply throught the parentheses:

    \frac{2}{3}(12t - 18) +2t -30 = \left(\frac{2}{3}\right)(12t) - \left(\frac{2}{3}\right)(18) + 2t - 30 = 8t -12 +2t - 30

    Then you can just add like terms:

    8t -12 +2t - 30 = 10t -42
    Continuing from here, asuming you want to find the zeros of the function f(t) = \frac{2}{3}(12t - 18) +2t -30

    f(t) = 10t - 42

    0 = 10t - 42

    42 = 10t

    t = \frac{42}{10} = \frac{21}{5} = 4.2

    Edit: Ignore all of this. I was confused by the OP's edit and thought that he or she wanted to solve the original expressions posted.
    Last edited by sinewave85; March 11th 2009 at 08:39 PM.
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  6. #6
    Member sinewave85's Avatar
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    Quote Originally Posted by Uriah5356 View Post
    For which question, those are two individual questions.
    Ok, after rereading: The first two expressions you only need to simplify, the second set you need to solve, right?
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  7. #7
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Uriah5356 View Post

    2 - (4x + 7) = 3 + 2 (x + 2) ------ I started solving this one by using distributive property after adding 3+2=5 on the right side, making (x + 2) into 5x + 10..?

    x/3 + x/4 = -2 ------ This one I started by getting the least common denominator of 3 and 4, which made the equation 4x/12 + 3x/12 = 7x/12 ------ From there it left me with 7x/12 = -2 and from there I am stuck.
    2 - 4x - 7 = 3+2x+4 (multiplying comes before addition)

    6x = -12
    x = -12/6 = -2

    ----

    From 7x/12 = -2 all you need to do it multiply -2 by 12/7
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  8. #8
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    Quote Originally Posted by sinewave85 View Post
    Ok, after rereading: The first two expressions you only need to simplify, the second set you need to solve, right?
    Right!
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  9. #9
    Member sinewave85's Avatar
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    Quote Originally Posted by Uriah5356 View Post
    Right!
    Ok, now we are talking! First lets tackle the simplifications. Did you understand my first post?
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  10. #10
    Member sinewave85's Avatar
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    Quote Originally Posted by sinewave85 View Post
    First you need to multiply throught the parentheses:

    \frac{2}{3}(12t - 18) +2t -30 = \left(\frac{2}{3}\right)(12t) - \left(\frac{2}{3}\right)(18) + 2t - 30 = 8t -12 +2t - 30

    Then you can just add like terms:

    8t -12 +2t - 30 = 10t -42
    Lets pick up again from here. Sorry about the confusion. The key to simplifying the first two expressions is the distributive property, which is very nicely explained here: Distributive Property - Free Math Help. After that, it is just a matter of adding like terms.
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  11. #11
    Member sinewave85's Avatar
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    Here is the second expression simplified:

    40\left(\frac{3}{8}Y - \frac{1}{4}\right) + 40\left(\frac{4}{5}\right) = 40\left(\frac{3}{8}Y\right) - 40\left(\frac{1}{4}\right) + 40\left(\frac{4}{5}\right) = 15Y - 10 + 32 = 15Y +22

    Unfortunately, I don't have time to completely go through the third and fourth problems, but e^(i*pi) did a nice job of typing them out. You need to review how the distributive property relates to the order of opperations --why you can't add the 3 and the 2 outside the parentheses first here: 3 + 2(x + 2)\not= 5(x +2) . I think that website I put up the link to will help. If this can wait untill tomorrow, I can work with you more then. Just reply and let me know where you are at.
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  12. #12
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    Thanks for the help on these problems. :< I will be up for awhile so I might have more.
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  13. #13
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    Quote Originally Posted by e^(i*pi) View Post
    2 - 4x - 7 = 3+2x+4 (multiplying comes before addition)

    6x = -12
    x = -12/6 = -2

    ----

    From 7x/12 = -2 all you need to do it multiply -2 by 12/7

    Why reverse 7/12 to 12/7 to multiply? o.o
    Am I correct in getting -24/7 ?
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  14. #14
    Member sinewave85's Avatar
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    Quote Originally Posted by Uriah5356 View Post
    Why reverse 7/12 to 12/7 to multiply? o.o
    Am I correct in getting -24/7 ?
    Because you are really not multiplying, you are dividing both sides of the equation by 7/12 (because division undoes the multiplication by 7/12 on the left side of the equation). But to divide by a fraction, you invert the fraction (swap the numerator and the divisor) and rewrite the division as a multiplication like this:

    \frac{7x}{12} = -2

    \frac{\frac{7x}{12}}{\frac{7}{12}} = \frac{-2}{\frac{7}{12}}



    \left(\frac{7x}{12}\right)\left(\frac{12}{7}\right  ) = \left(-2\right)\left(\frac{12}{7}\right)

    \mbox{note}\uparrow\mbox{how dividing 7/12 by itself cancels it out and leaves x by itself}

    x = \frac{-24}{7}

    Yes, you are correct in getting -27/7 .

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