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Math Help - SAT algebra equation

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    Senior Member vaironxxrd's Avatar
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    SAT algebra equation

    Hello Guys i was doing a Algebra SAT question.. and it was logical so i believe i got the right answer but in the future i don't want to get confuse so is there anyway to set an equation for this ?.

    If 2x+2x+2x+2x=12 Then what is 2x-1=

    I got that X is 2 because 2.2=4,2.2=4 2.2=4 =12 so 2.2-1=3

    But i really don't know what would i ahve done if it was a bigger number..
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    A Plied Mathematician
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    \underbrace{2x+2x+2x+2x}_{\text{Are there 3 or 4 of these?}}=12.
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    MHF Contributor harish21's Avatar
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    2x+2x+2x+2x=12 \implies 8x=12 \implies x=\dfrac{12}{8}

    now find 2x-1
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    A Plied Mathematician
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    Incidentally, you're in the right forum.
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    Senior Member vaironxxrd's Avatar
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    Quote Originally Posted by Ackbeet View Post
    \underbrace{2x+2x+2x+2x}_{\text{Are there 3 or 4 of these?}}=12.
    I got the book home but i am pretty sure is 3 of them because when i got 12 the only answer could been 3, 4's
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    Senior Member vaironxxrd's Avatar
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    [Math]\implies x=\dfrac{12}{8}[/tex] . You get 1.5
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    It makes a big difference if there are three or four of them. If there are three, then you're correct, and x = 2. You also correctly computed 2x-1, although your notation of using '.' for multiplication is not a good one for numbers. Use the asterisk: * for multiplication.

    But i really don't know what would i ahve done if it was a bigger number..
    If what was a bigger number?
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    The question should have 2x+2x+2x=12.

    Simple strategy: "Take a guess"

    Try to take a reasonable guess for x. Let's try x=3. Then 2(3) + 2(3) + 2(3) = 6+6+6=18, too big.

    So let's try x=2. Then 2(2)+2(2)+2(2) = 4+4+4=12. Just right.

    So x=2 and 2x-1=2(2)-1=4-1=3.

    Note that you can do all of these computations quickly in your calculator.

    After you're comfortable with the method of "guessing", also try to solve the problem algebraically.
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    Senior Member vaironxxrd's Avatar
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    Quote Originally Posted by harish21 View Post
    2x+2x+2x+2x=12 \implies 8x=12 \implies x=\dfrac{12}{8}

    now find 2x-1
    Quote Originally Posted by Ackbeet View Post
    It makes a big difference if there are three or four of them. If there are three, then you're correct, and x = 2. You also correctly computed 2x-1, although your notation of using '.' for multiplication is not a good one for numbers. Use the asterisk: * for multiplication.



    If what was a bigger number?
    if that 2 and the 12 where bigger, is there any Equation i could use?
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    Senior Member vaironxxrd's Avatar
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    Quote Originally Posted by DrSteve View Post
    The question should have 2x+2x+2x=12.

    Simple strategy: "Take a guess"

    Try to take a reasonable guess for x. Let's try x=3. Then 2(3) + 2(3) + 2(3) = 6+6+6=18, too big.

    So let's try x=2. Then 2(2)+2(2)+2(2) = 4+4+4=12. Just right.

    So x=2 and 2x-1=2(2)-1=4-1=3.

    Note that you can do all of these computations quickly in your calculator.

    After you're comfortable with the method of "guessing", also try to solve the problem algebraically.
    Yea i did it over the method of logic , and guessing
    but im trying to find it algebraically now
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    Quote Originally Posted by vaironxxrd View Post
    if that 2 and the 12 where bigger, is there any Equation i could use?
    Well, there's no equation. But there is a procedure:

    3x+3x+3x=21

    9x=21

    x=\dfrac{21}{9}=\dfrac{7}{3}.

    Then plug into your 2x-1 expression to obtain

    2\left(\dfrac{7}{3}\right)-1=\dots
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    Senior Member vaironxxrd's Avatar
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    Quote Originally Posted by Ackbeet View Post
    Well, there's no equation. But there is a procedure:

    3x+3x+3x=21

    9x=21

    x=\dfrac{21}{9}=\dfrac{7}{3}.

    Then plug into your 2x-1 expression to obtain

    2\left(\dfrac{7}{3}\right)-1=\dots

    I see you simplified the fraction So that would be 2*7 and 2*3 -1?
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  13. #13
    MHF Contributor Unknown008's Avatar
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    If you know how to factorise, you can make it a little simpler.

    2x + 2x + 2x + 2x = 12

    x(2 + 2 + 2 + 2) = 12

    What is 2 + 2 + 2 + 2? It's 8 of course!

    Then, x*8 = 12

    x = 12/8 = 1.5

    You can apply the same procedure for bigger numbers.
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    Quote Originally Posted by vaironxxrd View Post
    I see you simplified the fraction So that would be 2*7 and 2*3 -1?
    No, no. You multiply the scalar 2 times the fraction 7/3. THEN you add the fractions by getting a common denominator.
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    Senior Member vaironxxrd's Avatar
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    Quote Originally Posted by Unknown008 View Post
    If you know how to factorise, you can make it a little simpler.

    2x + 2x + 2x + 2x = 12

    x(2 + 2 + 2 + 2) = 12

    What is 2 + 2 + 2 + 2? It's 8 of course!

    Then, x*8 = 12

    x = 12/8 = 1.5

    You can apply the same procedure for bigger numbers.
    yea it is 1.5 But if you do 2*1.5 you get 3 not 2*1.5-1
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