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Math Help - Help a Dummy Figure Out An Easy Equation!

  1. #1
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    Help a Dummy Figure Out An Easy Equation!

    Stupid me forgot how to solve equations with two variables. I tried finding a tutorial of some sort on the internet but I can't find one like the question I present to you here:

    2 + 14x = 9x

    For some reason I can't seem to find any tutorials on questions where the variable is on both sides of the = sign. Please help! I have absolutely no clue how to start off the solving process.
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  2. #2
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    Quote Originally Posted by SomeRandomPerson View Post
    Stupid me forgot how to solve equations with two variables. I tried finding a tutorial of some sort on the internet but I can't find one like the question I present to you here:

    2 + 14x = 9x

    2 + 14x - 14x = 9x - 14x

    2 = -5x

    can you finish?


    For some reason I can't seem to find any tutorials on questions where the variable is on both sides of the = sign. Please help! I have absolutely no clue how to start off the solving process.
    ...
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  3. #3
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    Quote Originally Posted by SomeRandomPerson View Post
    Stupid me forgot how to solve equations with two variables. I tried finding a tutorial of some sort on the internet but I can't find one like the question I present to you here:

    2 + 14x = 9x

    For some reason I can't seem to find any tutorials on questions where the variable is on both sides of the = sign. Please help! I have absolutely no clue how to start off the solving process.
    Write 14x in terms of 9x

    2+14x=9x

    2+5x+9x=9x

    (2+5x)+9x=0+9x

    2+5x=0
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    @skeeter: Thanks for the reply. I can finish it off, I think:

    -5/2 = -2.5

    x = -2.5

    Is that right?

    I'll do another one, please tell me if I'm wrong:

    7x - 3 = 4x

    3 - 7x + 7x = 4x + 7x

    3 = 11x

    3/11 = 3.66667

    x = 3.66667

    I really do appreciate the help! Please do tell me if i did it right.

    Edit: Didn't see your reply there Archie. I'm not quite understanding your approach. Where did the 0 come from?

    Another edit: I'm really confused now. From what I took from you skeeter, I got -2.5. But if I replace x with 2.5, the equation doesn't make sense:

    2 + 14x = 9x

    2 + 14(-2.5) = 9(-2.5)

    2 + -35 = -22.5

    -33 = -22.5

    Obviously -33 isn't the same as -22.5... sorry if I'm missing something, I'm really having a hard time understanding this.
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  5. #5
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    -5x = 2

    x = -2/5 not -2.5
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    Does that mean for my second equation that I posted above the answer would be 3/11?

    Also, what does a number with a slash represent? Is it like a fraction? I thought a slash meant to divide.
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  7. #7
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    Quote Originally Posted by SomeRandomPerson View Post
    @skeeter: Thanks for the reply. I can finish it off, I think:

    -5/2 = -2.5

    2=-5x

    Divide both sides by -5

    x=-2/5=-0.4

    x = -2.5

    Is that right?

    I'll do another one, please tell me if I'm wrong:

    7x - 3 = 4x

    3 - 7x + 7x = 4x + 7x

    You should have 7x-3=4x

    7x-4x-3=4x-4x

    3x-3=0

    3x=3

    3 = 11x

    3/11 = 3.66667

    x = 3.66667

    I really do appreciate the help! Please do tell me if i did it right.

    Edit: Didn't see your reply there Archie. I'm not quite understanding your approach. Where did the 0 come from?

    We can say 4+0=4, x+0=x, adding zero does not change any value, therefore the 2+5x had to be 0

    Another edit: I'm really confused now. From what I took from you skeeter, I got -2.5. But if I replace x with 2.5, the equation doesn't make sense:

    2 + 14x = 9x

    2 + 14(-2.5) = 9(-2.5)

    2 + -35 = -22.5

    -33 = -22.5

    Obviously -33 isn't the same as -22.5... sorry if I'm missing something, I'm really having a hard time understanding this.
    .
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  8. #8
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    Quote Originally Posted by SomeRandomPerson View Post
    Does that mean for my second equation that I posted above the answer would be 3/11?

    Also, what does a number with a slash represent? Is it like a fraction? I thought a slash meant to divide.
    2/5 is the same as \frac{2}{5} is the same as 2 \div 5

    you need some lessons ... go through all 4 pages of the following link

    http://www.purplemath.com/modules/solvelin.htm
    Last edited by skeeter; October 6th 2010 at 07:00 PM. Reason: add link
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    @Skeeter: Thanks a bunch for your help, and for the link. I will look at it.
    @Archie: I get your 0 approach now. I'm a little confused about this though:

    You should have 7x-3=4x

    7x-4x-3=4x-4x

    3x-3=0

    3x=3
    So x = 1 which is fine with me. But I'm confused as to how to start the equation. I thought you just move the number over and then do the opposite operation, which is why I used addition. Basically, my question is how do you start it, and how do you know which operation to use? What order do you put it in? How would I know what order to put it in?

    Gah, I never thought such simple questions would cause so many problems with me!
    Last edited by SomeRandomPerson; October 6th 2010 at 07:22 PM.
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  10. #10
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    Quote Originally Posted by SomeRandomPerson View Post
    @Skeeter: Thanks a bunch for your help, and for the link. I will look at it.
    @Archie: I get your 0 approach now. I'm a little confused about this though:



    So x = 1 which is fine with me. But I'm confused as to how to start the equation. I thought you just move the number over and then do the opposite operation, which is why I used addition.

    But you didn't do the opposite operation for the 7x. Let's look at that....

    7x-3=4x

    You want to find x. If we subtract 4x from both sides, we will get x on one side only

    +7x-3=+4x

    +7x-3-4x=+4x-4x

    7x-4x-3=0

    You can do that more quickly by bringing 4x to the other side and changing it's sign.

    7x-3=4x

    7x-4x-3=0

    so we get 3x-3=0

    Alternatively, you can subtract 7x from both sides

    7x-3=4x

    7x-7x-3=4x-7x

    -3=-3x


    Basically, my question is how do you start it, and how do you know which operation to use? What order do you put it in? How would I know what order to put it in?

    You simply perform the OPPOSITE OPERATION on the x term you want to move.

    7x-3=4x

    +7x-3=0+4x

    If you want to bring the x's together, you can subtract 4x from both sides to get no x on the right
    or subtract 7x from both sides to get no x on the left.

    Alternatively, write 7x as 3x+4x

    7x-3=4x

    3x+4x-3=4x

    4x+(3x-3)=4x+0

    3x-3=0

    Two values are equal, when you subtract them the answer is 0.

    3x=3

    3(1)=3 so x=1, or divide both sides by 3.

    Multiplying x by 3 gives 3, so perform the opposite operation. Divide both sides by 3 to get x.

    3x=3

    3x/3=3/3

    x(3/3)=3/3

    x(1)=1 so x=1


    Gah, I never thought such simple questions would cause so many problems with me!
    .
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