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simple equation

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Jeff Bezos
19/03/2017 at 01:00
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When n is added to each numerator of \(\dfrac{2}{3},\dfrac{m}{4}\)and \(\dfrac{n}{6},\)the sum of the new fractions is 6. Find the value of m x n

simple equation

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    Kudo Shinichi 21/03/2017 at 22:40

    Ta có : 

    \(\dfrac{2}{3}+\dfrac{m}{4}+\dfrac{n}{6}=6\Rightarrow\dfrac{m}{4}+\dfrac{n}{6}=5\dfrac{1}{3}\)

    => m/4 = 2/6 = 2/3

    m/4 = 16/3 : ( 3+2 ) x 2 = 32/15

    n/6 = 16/3-32/15 = 16/5

    => m x n = 32 x 16 = 512

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  • ...
    FA KAKALOTS 03/02/2018 at 12:39

    Ta có : 

    23+m4+n6=6⇒m4+n6=513

    => m/4 = 2/6 = 2/3

    m/4 = 16/3 : ( 3+2 ) x 2 = 32/15

    n/6 = 16/3-32/15 = 16/5

    => m x n = 32 x 16 = 512

  • ...
    Tạ Đức Duy 23/06/2017 at 23:12

    why m/4 =2/6=2/3 what what ?? i think you wrong ;(


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Jeff Bezos
19/03/2017 at 00:59
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Solve for the value of m in \(\dfrac{2a}{b+c}=\dfrac{2b}{a+c}=\dfrac{2c}{a+b}=m.\)

simple equation

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    Hồ Thu Giang 19/03/2017 at 09:36

    - If a + b + c \(\ne\)0 then

    \(\dfrac{2a}{b+c}=\dfrac{2b}{a+c}=\dfrac{2c}{a+b}=\dfrac{2a+2b+2c}{b+c+a+c+a+b}=\dfrac{2a+2b+2c}{2a+2b+2c}=1\)

    => \(m=1\)

    - If a + b + c = 0 then

    b + c = -a

    a + c = -b

    a + b = -c

    => \(\dfrac{2a}{b+c}=\dfrac{2b}{a+b}=\dfrac{2c}{a+b}=\dfrac{2a}{-a}=\dfrac{2b}{-b}=\dfrac{2c}{-c}=-2\)

    => \(m=-2\)

    Jeff Bezos selected this answer.
  • ...
    FA KAKALOTS 03/02/2018 at 12:39

    - If a + b + c ≠

    0 then

    2ab+c=2ba+c=2ca+b=2a+2b+2cb+c+a+c+a+b=2a+2b+2c2a+2b+2c=1

    => m=1

    - If a + b + c = 0 then

    b + c = -a

    a + c = -b

    a + b = -c

    => 2ab+c=2ba+b=2ca+b=2a−a=2b−b=2c−c=−2

    => m=−2


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Jeff Bezos
19/03/2017 at 00:58
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Express y in terms of x in \(\dfrac{3-x}{5}+\dfrac{x+y}{10}=\dfrac{x-y}{4}.\)

simple equation

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    Phan Thanh Tinh Coordinator 23/03/2017 at 18:29

    \(\dfrac{3-x}{5}+\dfrac{x+y}{10}=\dfrac{x-y}{4}\)

    \(\Leftrightarrow\dfrac{12-4x}{20}+\dfrac{2x+2y}{20}=\dfrac{5x-5y}{20}\)

    \(\Leftrightarrow12-4x+2x+2y=5x-5y\)

    \(\Leftrightarrow2y+5y=5x+4x-2x-12\)

    \(\Leftrightarrow7y=7x-12\Leftrightarrow y=x-\dfrac{12}{7}\)

    Selected by MathYouLike
  • ...
    FA KAKALOTS 03/02/2018 at 12:40

    3−x5+x+y10=x−y4

    ⇔12−4x20+2x+2y20=5x−5y20

    ⇔12−4x+2x+2y=5x−5y

    ⇔2y+5y=5x+4x−2x−12

    ⇔7y=7x−12⇔y=x−127


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Jeff Bezos
19/03/2017 at 00:57
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If x = 3 satisfies \(\dfrac{a-x}{3}=\dfrac{bx-5}{5}\), find the value of \(\dfrac{a}{b}-\dfrac{b}{a}\) 

simple equation

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    Hồ Thu Giang 19/03/2017 at 09:42

    If x = 3

    => \(\dfrac{a-3}{3}=\dfrac{3b-5}{5}\)

    => \(5\left(a-3\right)=3\left(3b-5\right)\)

    => 5a - 15 = 9b - 15

    => 5a = 9b

    => \(\dfrac{a}{b}=\dfrac{9}{5}\)

    => \(\dfrac{b}{a}=\dfrac{5}{9}\)

    => \(\dfrac{a}{b}-\dfrac{b}{a}=\dfrac{9}{5}-\dfrac{5}{9}=\dfrac{56}{45}\)

    Jeff Bezos selected this answer.
  • ...
    FA KAKALOTS 03/02/2018 at 12:40

    If x = 3

    => a−33=3b−55

    => 5(a−3)=3(3b−5)

    => 5a - 15 = 9b - 15

    => 5a = 9b

    => ab=95

    => ba=59

    => ab−ba=95−59=5645


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Jeff Bezos
19/03/2017 at 00:54
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If x = 1 is the solution for px + 4q = 161, where both p and q are primes, find the value of p2 - q.

simple equation

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    FA KAKALOTS 03/02/2018 at 12:40

    i will you to make this topic :)
    replace x=1 into the polution above , we have 
    p+4q=161 
    => q= (161-p)/4 
    => q=40-(p-1)/4 => q<40(1)
    because the p and q are primes so (p-1) divisible for 4 =>p-1 >=4 => p>=5 (2)
    Merged (1) with (2) we have q ={2;3;5;7;11;13;17;19;23;29;31}
    then you try to the each of case : it will have 2 cases (correct satisfies) 
    this case p=37 <=> q=31 and p=133 <=> q=7

  • ...
    Tạ Đức Duy 23/06/2017 at 23:10

    i will you to make this topic :)
    replace x=1 into the polution above , we have 
    p+4q=161 
    => q= (161-p)/4 
    => q=40-(p-1)/4 => q<40(1)
    because the p and q are primes so (p-1) divisible for 4 =>p-1 >=4 => p>=5 (2)
    Merged (1) with (2) we have q ={2;3;5;7;11;13;17;19;23;29;31}
    then you try to the each of case : it will have 2 cases (correct satisfies) 
    this case p=37 <=> q=31 and p=133 <=> q=7 


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Jeff Bezos
19/03/2017 at 00:53
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An operation is defined as a*b = 3*a - 5*b.

Find the value of x in 7*(x*4) = 1.

simple equation

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    Phan Thanh Tinh Coordinator 23/03/2017 at 18:31

    We have : 7*(x*4) = 7*(3x - 20) = 21 - 5(3x - 20) = 121 - 15x

    So 121 - 15x = 1 => 15x = 120 => x = 8

    Selected by MathYouLike

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Jeff Bezos
19/03/2017 at 00:51
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Solve for the value of x in (x+2) : 2 = (5x-8) : 4

simple equation

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    Hồ Thu Giang 19/03/2017 at 09:46

    (x + 2) : 2 = (5x - 8) : 4

    => \(\dfrac{x+2}{2}=\dfrac{5x-8}{4}\)

    <=> 4(x + 2) = 2(5x - 8)

    <=> 4x + 8 = 10x - 16

    => 24 = 6x

    => x = 4

    Jeff Bezos selected this answer.
  • ...
    FA KAKALOTS 03/02/2018 at 12:41

    (x + 2) : 2 = (5x - 8) : 4

    => x+22=5x−84

    <=> 4(x + 2) = 2(5x - 8)

    <=> 4x + 8 = 10x - 16

    => 24 = 6x

    => x = 4


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Jeff Bezos
19/03/2017 at 00:47
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Solve for the value of x when 17x - 85 = 85 - 17x

simple equation

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    Phan Thanh Tinh Coordinator 23/03/2017 at 18:32

    17x - 85 = 85 - 17x

    <=> 17x + 17x = 85 + 85

    <=> 34x           = 170

    <=> x               = 5

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  • ...
    FA KAKALOTS 03/02/2018 at 12:41

    17x - 85 = 85 - 17x

    <=> 17x + 17x = 85 + 85

    <=> 34x           = 170

    <=> x               = 5


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mark zuckerberg
19/03/2017 at 00:45
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what can be the smallest value of a in 6x - a = 5x + 8?

simple equation


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mark zuckerberg
19/03/2017 at 00:40
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If an operation is defined as a*b = 3a-b, the value of x in x * (1*2) = 2 is

simple equation

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    Phan Thanh Tinh Coordinator 23/03/2017 at 18:35

    We have : x*(1*2) = x*(3 - 2) = x*1 = 3x - 1

    So 3x - 1 = 2 => 3x = 3 => x = 1

    Selected by MathYouLike

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mark zuckerberg
19/03/2017 at 00:37
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The value of x in

\(\dfrac{x}{1\times2}+\dfrac{x}{2\times3}+\dfrac{x}{3\times4}+...+\dfrac{x}{1999\times2000}=1\)is?

simple equation

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    Phan Thanh Tinh Coordinator 23/03/2017 at 18:39

    \(\dfrac{x}{1.2}+\dfrac{x}{2.3}+\dfrac{x}{3.4}+...+\dfrac{x}{1999.2000}=1\)

    \(x\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{1999.2000}\right)=1\)

    \(x\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{1999}-\dfrac{1}{2000}\right)=1\)

    \(x\left(1-\dfrac{1}{2000}\right)=1\)

    \(x.\dfrac{1999}{2000}=1\)

    \(x=\dfrac{2000}{1999}\)

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  • ...
    FA KAKALOTS 03/02/2018 at 12:41

    x1.2+x2.3+x3.4+...+x1999.2000=1

    x(11.2+12.3+13.4+...+11999.2000)=1

    x(1−12+12−13+13−14+...+11999−12000)=1

    x(1−12000)=1

    x.19992000=1

    x=20001999


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mark zuckerberg
19/03/2017 at 00:36
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If \(\dfrac{a-b}{b}=\dfrac{3}{5}\), the value of \(\dfrac{a}{b}\) is?

simple equation

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    Phan Thanh Tinh Coordinator 23/03/2017 at 18:40

    \(\dfrac{a-b}{b}=\dfrac{a}{b}-1\).So\(\dfrac{a}{b}-1=\dfrac{3}{5}\Rightarrow\dfrac{a}{b}=\dfrac{8}{5}\)


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mark zuckerberg
19/03/2017 at 00:34
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If x = 2 satisfies the equation px+q=91 and p-q=2, the value of pq is ?

simple equation

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    Phan Thanh Tinh Coordinator 23/03/2017 at 18:44

    Replace x = 2 into the given equations,we have :

    \(\left\{{}\begin{matrix}2p+q=91\\p-q=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2p+p-2=91\\q=p-2\end{matrix}\right.\)

    \(\Rightarrow\left\{{}\begin{matrix}3p=93\\q=p-2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}p=31\\q=29\end{matrix}\right.\)=> pq = 899

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  • ...
    FA KAKALOTS 03/02/2018 at 12:42

    Replace x = 2 into the given equations,we have :

    {2p+q=91p−q=2⇒{2p+p−2=91q=p−2

    ⇒{3p=93q=p−2⇒{p=31q=29

    => pq = 899


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Nguyễn Đức Mạnh
17/03/2017 at 10:37
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3
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Solve \(\dfrac{13}{6}\left(x-3\right)+\dfrac{4}{3}\left(3-x\right)=\dfrac{7}{6}\left(x-3\right)+8\)

simple equation

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    mathlove 17/03/2017 at 10:52

    It is very easy. the done equation is writend as   \(\left(x-3\right)\left(\dfrac{13}{6}-\dfrac{4}{3}-\dfrac{7}{6}\right)=8\)

    \(\Leftrightarrow-\dfrac{1}{3}\left(x-3\right)=8\Leftrightarrow x=-21\) .

    Selected by MathYouLike
  • ...
    FA KAKALOTS 03/02/2018 at 12:42

    It is very easy. the done equation is writend as   (x−3)(136−43−76)=8

    ⇔−13(x−3)=8⇔x=−21

     .

  • ...
    Ace Legona 17/03/2017 at 11:53

    @mathlove: \(3-x\ne x-3\) ???


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Nguyễn Đức Mạnh
17/03/2017 at 10:36
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if (a+1) satisfies 2(x+1) = 3(x-1), find the solution to 2[3(2+x)-2(a-x)]=4a

simple equation

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    mathlove 17/03/2017 at 11:02

    Because (a+1) satisfies 2(x+1)=3(x-1), so that 2(a+1+1)=3a , a = 4.

    With a = 4, the equation to solve become  2[3(2+x) - 2(4-x)] = 16 , then x = 2.

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  • ...
    FA KAKALOTS 03/02/2018 at 12:42

    Because (a+1) satisfies 2(x+1)=3(x-1), so that 2(a+1+1)=3a , a = 4.

    With a = 4, the equation to solve become  2[3(2+x) - 2(4-x)] = 16 , then x = 2.


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Nguyễn Đức Mạnh
17/03/2017 at 10:35
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Find the smallest possible value of a, where a is a whole number, in

\(\dfrac{33x}{2}-a=\)\(\dfrac{5x}{6}+184\)

simple equation


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Nguyễn Đức Mạnh
17/03/2017 at 10:33
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Find the value of m if x = 3 satisfies the equation

\(\dfrac{m-x}{3}\)+\(\dfrac{3x-6}{4}\)=\(\dfrac{4x+5}{12}\)

simple equation

  • ...
    FA KAKALOTS 03/02/2018 at 12:42

    Replace x = 3 into the equation,we have :

    m−33+34=1712⇔m3−1=23⇔m3=53⇔m=5

  • ...
    Phan Thanh Tinh Coordinator 23/03/2017 at 19:50

    Replace x = 3 into the equation,we have :

    \(\dfrac{m-3}{3}+\dfrac{3}{4}=\dfrac{17}{12}\Leftrightarrow\dfrac{m}{3}-1=\dfrac{2}{3}\Leftrightarrow\dfrac{m}{3}=\dfrac{5}{3}\Leftrightarrow m=5\)


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Nguyễn Đức Mạnh
17/03/2017 at 10:31
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it is given 3 - a = 4 - b = 2, c = 499 . Also, a+b+c = 2008m. Find the value of m

simple equation

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    Phan Thanh Tinh Coordinator 23/03/2017 at 19:51

    3 - a = 4 - b = 2 => a = 1 ; b = 2 => a + b + c = 502

    => m =\(\dfrac{502}{2008}=\dfrac{1}{4}\)

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Nguyễn Đức Mạnh
17/03/2017 at 10:29
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if x = \(\dfrac{1}{2}\)statisfies the equation 4x - 3a = 0, find the value of a.

simple equation

  • ...
    duong312a 18/03/2017 at 12:14

    a = \(\dfrac{2}{3}\)

    2/3 nhé

    tk nhé

  • ...
    »ﻲ†hïếu๖ۣۜGïลﻲ« 26/03/2017 at 10:25

    Replacing x = 1/2 we have: 4x - 3a = 0  

    Have 4.1/2 - 3a = 0

     Have 2 - 3a = 0

     Have 3a = 2

     Has a = 2/3

    Dress a = 2/3 good

  • ...
    Love people Name Jiang 17/03/2017 at 18:51

    Replacing x = 1/2 we have: 4x - 3a = 0  

    <=> 4.1/2 - 3a = 0

    => 2 - 3a = 0

    => 3a = 2

    => a = 2/3

    Dress a = 2/3 good


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