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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
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation （200-382.4）/(200-500) = (9-x)/(9-20.9) .
Question type: Equation
Solution:Original question:
| ( | 200 | − | 1912 5 | ) | ÷ | ( | 200 | − | 500 | ) | = | ( | 9 | − | x | ) | ÷ | ( | 9 | − | 209 10 | ) |
| Multiply both sides of the equation by: | ( | 200 | − | 500 | ) | , | ( | 9 | − | 209 10 | ) |
| ( | 200 | − | 1912 5 | ) | ( | 9 | − | 209 10 | ) | = | ( | 9 | − | x | ) | ( | 200 | − | 500 | ) |
| 200 | ( | 9 | − | 209 10 | ) | − | 1912 5 | ( | 9 | − | 209 10 | ) | = | ( | 9 | − | x | ) | ( | 200 | − | 500 | ) |
| 200 | ( | 9 | − | 209 10 | ) | − | 1912 5 | ( | 9 | − | 209 10 | ) | = | 9 | ( | 200 | − | 500 | ) | − | x | ( | 200 | − | 500 | ) |
| 200 | × | 9 | − | 200 | × | 209 10 | − | 1912 5 | ( | 9 | − | 209 10 | ) | = | 9 | ( | 200 | − | 500 | ) | − | x | ( | 200 | − | 500 | ) |
| 200 | × | 9 | − | 200 | × | 209 10 | − | 1912 5 | ( | 9 | − | 209 10 | ) | = | 9 | × | 200 | − | 9 | × | 500 | − | x | ( | 200 | − | 500 | ) |
| 1800 | − | 4180 | − | 1912 5 | ( | 9 | − | 209 10 | ) | = | 1800 | − | 4500 | − | x | ( | 200 | − | 500 | ) |
| - | 2380 | − | 1912 5 | ( | 9 | − | 209 10 | ) | = | - | 2700 | − | x | ( | 200 | − | 500 | ) |
| - | 2380 | − | 1912 5 | × | 9 | + | 1912 5 | × | 209 10 | = | - | 2700 | − | x | ( | 200 | − | 500 | ) |
| - | 2380 | − | 1912 5 | × | 9 | + | 1912 5 | × | 209 10 | = | - | 2700 | − | x | × | 200 | + | x | × | 500 |
| - | 2380 | − | 17208 5 | + | 199804 25 | = | - | 2700 | − | x | × | 200 | + | x | × | 500 |
54264 25 | = | - | 2700 | + | 300 | x |
Transposition :
| - | 300 | x | = | - | 2700 | − | 54264 25 |
Combine the items on the right of the equation:
| - | 300 | x | = | - | 121764 25 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
121764 25 | = | 300 | 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 :
| 300 | x | = | 121764 25 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 121764 25 | ÷ | 300 |
| = | 121764 25 | × | 1 300 |
| = | 10147 25 | × | 1 25 |
We obtained :
| x | = | 10147 625 |
Convert the result to decimal form :
| x | = | 16.2352 |