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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 ÷
19
2
)
     375(1 ÷ 50 + 1 ÷
19
2
+ 2 x ÷
1
10
+ x ÷
3
50
)(1 ÷
19
2
) = 25
    Remove a bracket on the left of the equation::
     375 × 1 ÷ 50 × (1 ÷
19
2
) + 375 × 1 ÷
19
2
× (1 ÷
19
2
) + 375 × 2 x ÷
1
10
= 25
    The equation is reduced to :
     
15
2
(1 ÷
19
2
) +
750
19
(1 ÷
19
2
) + 7500 x (1 ÷
19
2
) + 6250 x (1 ÷
19
2
) = 25
    Remove a bracket on the left of the equation:
     
15
2
× 1 ÷
19
2
+
750
19
(1 ÷
19
2
) + 7500 x (1 ÷
19
2
) + 6250 x (1 ÷
19
2
) = 25
    The equation is reduced to :
     
15
19
+
750
19
(1 ÷
19
2
) + 7500 x (1 ÷
19
2
) + 6250 x (1 ÷
19
2
) = 25
    Remove a bracket on the left of the equation:
     
15
19
+
750
19
× 1 ÷
19
2
+ 7500 x (1 ÷
19
2
) + 6250 x (1 ÷
19
2
) = 25
    The equation is reduced to :
     
15
19
+
1500
361
+ 7500 x (1 ÷
19
2
) + 6250 x (1 ÷
19
2
) = 25
    The equation is reduced to :
     
1785
361
+ 7500 x (1 ÷
19
2
) + 6250 x (1 ÷
19
2
) = 25
    Remove a bracket on the left of the equation:
     
1785
361
+ 7500 x × 1 ÷
19
2
+ 6250 x (1 ÷
19
2
) = 25
    The equation is reduced to :
     
1785
361
+
15000
19
x + 6250 x (1 ÷
19
2
) = 25
    Remove a bracket on the left of the equation:
     
1785
361
+
15000
19
x + 6250 x × 1 ÷
19
2
= 25
    The equation is reduced to :
     
1785
361
+
15000
19
x +
12500
19
x = 25
    The equation is reduced to :
     
1785
361
+
27500
19
x = 25

    Transposition :
     
27500
19
x = 25
1785
361

    Combine the items on the right of the equation:
     
27500
19
x =
7240
361

    The coefficient of the unknown number is reduced to 1 :
      x =
7240
361
÷
27500
19
        =
7240
361
×
19
27500
        =
362
19
×
1
1375

    We obtained :
      x =
362
26125
    This is the solution of the equation.

    Convert the result to decimal form :
      x = 0.013856



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