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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.
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    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−300)×(1−0.25)/3300 = ((x−300)×(1−0.25)−75)/3150 .
    Question type: Equation
    Solution:Original question:
     ( x − 300)(1 −
1
4
) ÷ 3300 = (( x − 300)(1 −
1
4
) − 75) ÷ 3150
    Remove the bracket on the left of the equation:
     Left side of the equation = x (1 −
1
4
) ×
1
3300
 − 300(1 −
1
4
) ×
1
3300
                                             = x (1 −
1
4
) ×
1
3300
 −
1
11
(1 −
1
4
)
                                             = x × 1 ×
1
3300
 − x ×
1
4
 ×
1
3300
 −
1
11
(1 −
1
4
)
                                             = x ×
1
3300
 − x ×
1
13200
 −
1
11
(1 −
1
4
)
                                             =
1
4400
 x −
1
11
(1 −
1
4
)
                                             =
1
4400
 x −
1
11
 × 1 +
1
11
 ×
1
4
                                             =
1
4400
 x −
1
11
 +
1
44
                                             =
1
4400
 x −
3
44
    The equation is transformed into :
     
1
4400
 x −
3
44
 = (( x − 300)(1 −
1
4
) − 75) ÷ 3150
    Remove the bracket on the right of the equation:
     Right side of the equation = ( x − 300)(1 −
1
4
) ×
1
3150
 − 75 ×
1
3150
                                               = ( x − 300)(1 −
1
4
) ×
1
3150
 −
1
42
                                               = x (1 −
1
4
) ×
1
3150
 − 300(1 −
1
4
) ×
1
3150
 −
1
42
                                               = x (1 −
1
4
) ×
1
3150
 −
2
21
(1 −
1
4
) −
1
42
                                               = x × 1 ×
1
3150
 − x ×
1
4
 ×
1
3150
 −
2
21
(1 −
1
4
) −
1
42
                                               = x ×
1
3150
 − x ×
1
12600
 −
2
21
(1 −
1
4
) −
1
42
                                               =
1
4200
 x −
2
21
(1 −
1
4
) −
1
42
                                               =
1
4200
 x −
2
21
 × 1 +
2
21
 ×
1
4
 −
1
42
                                               =
1
4200
 x −
2
21
 +
1
42
 −
1
42
                                               =
1
4200
 x −
2
21
    The equation is transformed into :
     
1
4400
 x −
3
44
 =
1
4200
 x −
2
21

    Transposition :
     
1
4400
 x −
1
4200
 x = -
2
21
 +
3
44

    Combine the items on the left of the equation:
      -
1
92400
 x = -
2
21
 +
3
44

    Combine the items on the right of the equation:
      -
1
92400
 x = -
25
924

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
     
25
924
 =
1
92400
 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
92400
 x =
25
924

    The coefficient of the unknown number is reduced to 1 :
      x =
25
924
 ÷
1
92400
        =
25
924
 × 92400
        = 25 × 100

    We obtained :
      x = 2500
    This is the solution of the equation.



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