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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 (0.25-x)/(0.25-0.075) = 10.1/(40.1-27.8) .
Question type: Equation
Solution:Original question:
| ( | 1 4 | − | x | ) | ÷ | ( | 1 4 | − | 3 40 | ) | = | 101 10 | ÷ | ( | 401 10 | − | 139 5 | ) |
| Multiply both sides of the equation by: | ( | 1 4 | − | 3 40 | ) | , | ( | 401 10 | − | 139 5 | ) |
| ( | 1 4 | − | x | ) | ( | 401 10 | − | 139 5 | ) | = | 101 10 | ( | 1 4 | − | 3 40 | ) |
1 4 | ( | 401 10 | − | 139 5 | ) | − | x | ( | 401 10 | − | 139 5 | ) | = | 101 10 | ( | 1 4 | − | 3 40 | ) |
1 4 | ( | 401 10 | − | 139 5 | ) | − | x | ( | 401 10 | − | 139 5 | ) | = | 101 10 | × | 1 4 | − | 101 10 | × | 3 40 |
1 4 | ( | 401 10 | − | 139 5 | ) | − | x | ( | 401 10 | − | 139 5 | ) | = | 101 40 | − | 303 400 |
1 4 | ( | 401 10 | − | 139 5 | ) | − | x | ( | 401 10 | − | 139 5 | ) | = | 707 400 |
1 4 | × | 401 10 | − | 1 4 | × | 139 5 | − | x | ( | 401 10 | − | 139 5 | ) | = | 707 400 |
401 40 | − | 139 20 | − | x | ( | 401 10 | − | 139 5 | ) | = | 707 400 |
123 40 | − | x | ( | 401 10 | − | 139 5 | ) | = | 707 400 |
123 40 | − | x | × | 401 10 | + | x | × | 139 5 | = | 707 400 |
123 40 | − | 123 10 | x | = | 707 400 |
Transposition :
| - | 123 10 | x | = | 707 400 | − | 123 40 |
Combine the items on the right of the equation:
| - | 123 10 | x | = | - | 523 400 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
523 400 | = | 123 10 | 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 :
123 10 | x | = | 523 400 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 523 400 | ÷ | 123 10 |
| = | 523 400 | × | 10 123 |
| = | 523 40 | × | 1 123 |
We obtained :
| x | = | 523 4920 |
Convert the result to decimal form :
| x | = | 0.106301 |