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On line Solution of Monovariate Equation：
    Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
    It supports equations that contain mathematical functions.
    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer

    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation (x-180)*(1-25%)/2400 = (x-450)(1-25%)/2000 .
    Question type: Equation
    Solution:Original question:
     ( x − 180)(1 −
25
100
) ÷ 2400 = ( x − 450)(1 −
25
100
) ÷ 2000
    Remove the bracket on the left of the equation:
     Left side of the equation = x (1 −
25
100
) ×
1
2400
 − 180(1 −
25
100
) ×
1
2400
                                             = x (1 −
25
100
) ×
1
2400
 −
3
40
(1 −
25
100
)
                                             = x × 1 ×
1
2400
 − x ×
25
100
 ×
1
2400
 −
3
40
(1 −
25
100
)
                                             = x ×
1
2400
 − x ×
1
9600
 −
3
40
(1 −
25
100
)
                                             =
1
3200
 x −
3
40
(1 −
25
100
)
                                             =
1
3200
 x −
3
40
 × 1 +
3
40
 ×
25
100
                                             =
1
3200
 x −
3
40
 +
3
160
                                             =
1
3200
 x −
9
160
    The equation is transformed into :
     
1
3200
 x −
9
160
 = ( x − 450)(1 −
25
100
) ÷ 2000
    Remove the bracket on the right of the equation:
     Right side of the equation = x (1 −
25
100
) ×
1
2000
 − 450(1 −
25
100
) ×
1
2000
                                               = x (1 −
25
100
) ×
1
2000
 −
9
40
(1 −
25
100
)
                                               = x × 1 ×
1
2000
 − x ×
25
100
 ×
1
2000
 −
9
40
(1 −
25
100
)
                                               = x ×
1
2000
 − x ×
1
8000
 −
9
40
(1 −
25
100
)
                                               =
3
8000
 x −
9
40
(1 −
25
100
)
                                               =
3
8000
 x −
9
40
 × 1 +
9
40
 ×
25
100
                                               =
3
8000
 x −
9
40
 +
9
160
                                               =
3
8000
 x −
27
160
    The equation is transformed into :
     
1
3200
 x −
9
160
 =
3
8000
 x −
27
160

    Transposition :
     
1
3200
 x −
3
8000
 x = -
27
160
 +
9
160

    Combine the items on the left of the equation:
      -
1
16000
 x = -
27
160
 +
9
160

    Combine the items on the right of the equation:
      -
1
16000
 x = -
9
80

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
     
9
80
 =
1
16000
 x

    If the left side of the equation is equal to the right side, then the right side must also be equal to the left side, that is :
     
1
16000
 x =
9
80

    The coefficient of the unknown number is reduced to 1 :
      x =
9
80
 ÷
1
16000
        =
9
80
 × 16000
        = 9 × 200

    We obtained :
      x = 1800
    This is the solution of the equation.



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