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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.
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
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[ 1/1 Equation]
Work: Find the solution of equation (x−7%)/(8%−7%) = (199.6−204.1)/(196.01−204.1) .
Question type: Equation
Solution:Original question:
| ( | x | − | 7 100 | ) | ÷ | ( | 8 100 | − | 7 100 | ) | = | ( | 998 5 | − | 2041 10 | ) | ÷ | ( | 19601 100 | − | 2041 10 | ) |
| Multiply both sides of the equation by: | ( | 8 100 | − | 7 100 | ) | , | ( | 19601 100 | − | 2041 10 | ) |
| ( | x | − | 7 100 | ) | ( | 19601 100 | − | 2041 10 | ) | = | ( | 998 5 | − | 2041 10 | ) | ( | 8 100 | − | 7 100 | ) |
| x | ( | 19601 100 | − | 2041 10 | ) | − | 7 100 | ( | 19601 100 | − | 2041 10 | ) | = | ( | 998 5 | − | 2041 10 | ) | ( | 8 100 | − | 7 100 | ) |
| x | ( | 19601 100 | − | 2041 10 | ) | − | 7 100 | ( | 19601 100 | − | 2041 10 | ) | = | 998 5 | ( | 8 100 | − | 7 100 | ) | − | 2041 10 | ( | 8 100 | − | 7 100 | ) |
| x | × | 19601 100 | − | x | × | 2041 10 | − | 7 100 | ( | 19601 100 | − | 2041 10 | ) | = | 998 5 | ( | 8 100 | − | 7 100 | ) | − | 2041 10 | ( | 8 100 | − | 7 100 | ) |
| x | × | 19601 100 | − | x | × | 2041 10 | − | 7 100 | ( | 19601 100 | − | 2041 10 | ) | = | 998 5 | × | 8 100 | − | 998 5 | × | 7 100 | − | 2041 10 | ( | 8 100 | − | 7 100 | ) |
| x | × | 19601 100 | − | x | × | 2041 10 | − | 7 100 | ( | 19601 100 | − | 2041 10 | ) | = | 1996 125 | − | 3493 250 | − | 2041 10 | ( | 8 100 | − | 7 100 | ) |
| - | 809 100 | x | − | 7 100 | ( | 19601 100 | − | 2041 10 | ) | = | 499 250 | − | 2041 10 | ( | 8 100 | − | 7 100 | ) |
| - | 809 100 | x | − | 7 100 | × | 19601 100 | + | 7 100 | × | 2041 10 | = | 499 250 | − | 2041 10 | ( | 8 100 | − | 7 100 | ) |
| - | 809 100 | x | − | 7 100 | × | 19601 100 | + | 7 100 | × | 2041 10 | = | 499 250 | − | 2041 10 | × | 8 100 | + | 2041 10 | × | 7 100 |
| - | 809 100 | x | − | 137207 10000 | + | 14287 1000 | = | 499 250 | − | 2041 125 | + | 14287 1000 |
| - | 809 100 | x | + | 5663 10000 | = | - | 9 200 |
Transposition :
| - | 809 100 | x | = | - | 9 200 | − | 5663 10000 |
Combine the items on the right of the equation:
| - | 809 100 | x | = | - | 6113 10000 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
6113 10000 | = | 809 100 | 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 :
809 100 | x | = | 6113 10000 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 6113 10000 | ÷ | 809 100 |
| = | 6113 10000 | × | 100 809 |
| = | 6113 100 | × | 1 809 |
We obtained :
| x | = | 6113 80900 |
Convert the result to decimal form :
| x | = | 0.075562 |