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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-20)(1-0.33)/15 = (x-20-40)(1-0.33)/10 .
    Question type: Equation
    Solution:Original question:
     ( x − 20)(1 −
33
100
) ÷ 15 = ( x − 20 − 40)(1 −
33
100
) ÷ 10
    Remove the bracket on the left of the equation:
     Left side of the equation = x (1 −
33
100
) ×
1
15
 − 20(1 −
33
100
) ×
1
15
                                             = x (1 −
33
100
) ×
1
15
 −
4
3
(1 −
33
100
)
                                             = x × 1 ×
1
15
 − x ×
33
100
 ×
1
15
 −
4
3
(1 −
33
100
)
                                             = x ×
1
15
 − x ×
11
500
 −
4
3
(1 −
33
100
)
                                             =
67
1500
 x −
4
3
(1 −
33
100
)
                                             =
67
1500
 x −
4
3
 × 1 +
4
3
 ×
33
100
                                             =
67
1500
 x −
4
3
 +
11
25
                                             =
67
1500
 x −
67
75
    The equation is transformed into :
     
67
1500
 x −
67
75
 = ( x − 20 − 40)(1 −
33
100
) ÷ 10
    Remove the bracket on the right of the equation:
     Right side of the equation = x (1 −
33
100
) ×
1
10
 − 20(1 −
33
100
) ×
1
10
 − 40(1 −
33
100
) ×
1
10
                                               = x (1 −
33
100
) ×
1
10
 − 2(1 −
33
100
) − 4(1 −
33
100
)
                                               = x × 1 ×
1
10
 − x ×
33
100
 ×
1
10
 − 2(1 −
33
100
) − 4(1 −
33
100
)
                                               = x ×
1
10
 − x ×
33
1000
 − 2(1 −
33
100
) − 4(1 −
33
100
)
                                               =
67
1000
 x − 2(1 −
33
100
) − 4(1 −
33
100
)
                                               =
67
1000
 x − 2 × 1 + 2 ×
33
100
 − 4(1 −
33
100
)
                                               =
67
1000
 x − 2 +
33
50
 − 4(1 −
33
100
)
                                               =
67
1000
 x −
67
50
 − 4(1 −
33
100
)
                                               =
67
1000
 x −
67
50
 − 4 × 1 + 4 ×
33
100
                                               =
67
1000
 x −
67
50
 − 4 +
33
25
                                               =
67
1000
 x −
201
50
    The equation is transformed into :
     
67
1500
 x −
67
75
 =
67
1000
 x −
201
50

    Transposition :
     
67
1500
 x −
67
1000
 x = -
201
50
 +
67
75

    Combine the items on the left of the equation:
      -
67
3000
 x = -
201
50
 +
67
75

    Combine the items on the right of the equation:
      -
67
3000
 x = -
469
150

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
     
469
150
 =
67
3000
 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 :
     
67
3000
 x =
469
150

    The coefficient of the unknown number is reduced to 1 :
      x =
469
150
 ÷
67
3000
        =
469
150
 ×
3000
67
        = 7 × 20

    We obtained :
      x = 140
    This is the solution of the equation.



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