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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 (20-x)/15 = 21.4/(81.4-50.1) .
Question type: Equation
Solution:Original question:
| ( | 20 | − | x | ) | ÷ | 15 | = | 107 5 | ÷ | ( | 407 5 | − | 501 10 | ) |
| Multiply both sides of the equation by: | ( | 407 5 | − | 501 10 | ) |
| ( | 20 | − | x | ) | ÷ | 15 | × | ( | 407 5 | − | 501 10 | ) | = | 107 5 |
| 20 | ÷ | 15 | × | ( | 407 5 | − | 501 10 | ) | − | x | ÷ | 15 | × | ( | 407 5 | − | 501 10 | ) | = | 107 5 |
4 3 | ( | 407 5 | − | 501 10 | ) | − | x | × | 1 15 | ( | 407 5 | − | 501 10 | ) | = | 107 5 |
4 3 | × | 407 5 | − | 4 3 | × | 501 10 | − | x | × | 1 15 | ( | 407 5 | − | 501 10 | ) | = | 107 5 |
1628 15 | − | 334 5 | − | x | × | 1 15 | ( | 407 5 | − | 501 10 | ) | = | 107 5 |
626 15 | − | x | × | 1 15 | ( | 407 5 | − | 501 10 | ) | = | 107 5 |
626 15 | − | x | × | 1 15 | × | 407 5 | + | x | × | 1 15 | × | 501 10 | = | 107 5 |
626 15 | − | x | × | 407 75 | + | x | × | 167 50 | = | 107 5 |
626 15 | − | 313 150 | x | = | 107 5 |
Transposition :
| - | 313 150 | x | = | 107 5 | − | 626 15 |
Combine the items on the right of the equation:
| - | 313 150 | x | = | - | 61 3 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
61 3 | = | 313 150 | 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 :
313 150 | x | = | 61 3 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 61 3 | ÷ | 313 150 |
| = | 61 3 | × | 150 313 |
| = | 61 | × | 50 313 |
We obtained :
| x | = | 3050 313 |
Convert the result to decimal form :
| x | = | 9.744409 |