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    Current location:Equations > Monovariate Equation > The history of univariate equation calculation > Answer

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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 375/(1/50+1/9.5+2x/0.1+x/0.06) = 25/(1/9.5) .
    Question type: Equation
    Solution:Original question:
     375 ÷ (1 ÷ 50 + 1 ÷
19
2
+ 2 x ÷
1
10
+ x ÷
3
50
) = 25 ÷ (1 ÷
19
2
)
     Multiply both sides of the equation by:(1 ÷ 50 + 1 ÷
19
2
+ 2 x ÷
1
10
+ x ÷
3
50
) ,  (1 ÷
19
2
)
     375(1 ÷
19
2
) = 25(1 ÷ 50 + 1 ÷
19
2
+ 2 x ÷
1
10
+ x ÷
3
50
)
    Remove a bracket on the left of the equation::
     375 × 1 ÷
19
2
= 25(1 ÷ 50 + 1 ÷
19
2
+ 2 x ÷
1
10
+ x ÷
3
50
)
    Remove a bracket on the right of the equation::
     375 × 1 ÷
19
2
= 25 × 1 ÷ 50 + 25 × 1 ÷
19
2
+ 25 × 2 x ÷
1
10
+ 25 x
    The equation is reduced to :
     
750
19
=
1
2
+
50
19
+ 500 x +
1250
3
x
    The equation is reduced to :
     
750
19
=
119
38
+
2750
3
x

    Transposition :
      -
2750
3
x =
119
38
750
19

    Combine the items on the right of the equation:
      -
2750
3
x = -
1381
38

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
     
1381
38
=
2750
3
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 :
     
2750
3
x =
1381
38

    The coefficient of the unknown number is reduced to 1 :
      x =
1381
38
÷
2750
3
        =
1381
38
×
3
2750

    We obtained :
      x =
4143
104500
    This is the solution of the equation.

    Convert the result to decimal form :
      x = 0.039646



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