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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
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Work: Find the solution of equation 10% = （8%*100/55*（1-x））/（1-8%*100/55*（1-x）） .
Question type: Equation
Solution:Original question:
10 100 | = | ( | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) | ) | ÷ | ( | 1 | − | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) | ) |
| Multiply both sides of the equation by: | ( | 1 | − | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) | ) |
10 100 | ( | 1 | − | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) | ) | = | ( | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) | ) |
10 100 | × | 1 | − | 10 100 | × | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) | = | ( | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) | ) |
10 100 | × | 1 | − | 10 100 | × | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) | = | 8 100 | × | 100 | ÷ | 55 | × | ( | 1 | − | x | ) |
1 10 | − | 4 275 | ( | 1 | − | x | ) | = | 8 55 | ( | 1 | − | x | ) |
1 10 | − | 4 275 | × | 1 | + | 4 275 | x | = | 8 55 | ( | 1 | − | x | ) |
1 10 | − | 4 275 | × | 1 | + | 4 275 | x | = | 8 55 | × | 1 | − | 8 55 | x |
1 10 | − | 4 275 | + | 4 275 | x | = | 8 55 | − | 8 55 | x |
47 550 | + | 4 275 | x | = | 8 55 | − | 8 55 | x |
Transposition :
4 275 | x | + | 8 55 | x | = | 8 55 | − | 47 550 |
Combine the items on the left of the equation:
4 25 | x | = | 8 55 | − | 47 550 |
Combine the items on the right of the equation:
4 25 | x | = | 3 50 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 3 50 | ÷ | 4 25 |
| = | 3 50 | × | 25 4 |
| = | 3 2 | × | 1 4 |
We obtained :
| x | = | 3 8 |
Convert the result to decimal form :
| x | = | 0.375 |