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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 1/2018(x+1)-x-1 = 2017 .
Question type: Equation
Solution:Original question:
| 1 | ÷ | 2018 | × | ( | x | + | 1 | ) | − | x | − | 1 | = | 2017 |
| Left side of the equation = | 1 2018 | ( | x | + | 1 | ) | − | x | − | 1 |
1 2018 | ( | x | + | 1 | ) | − | x | − | 1 | = | 2017 |
| Left side of the equation = | 1 2018 | x | + | 1 2018 | × | 1 | − | x | − | 1 |
| = | 1 2018 | x | + | 1 2018 | − | x | − | 1 |
| = | - | 2017 2018 | x | − | 2017 2018 |
| - | 2017 2018 | x | − | 2017 2018 | = | 2017 |
Transposition :
| - | 2017 2018 | x | = | 2017 | + | 2017 2018 |
Combine the items on the right of the equation:
| - | 2017 2018 | x | = | 4072323 2018 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
| - | 4072323 2018 | = | 2017 2018 | 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 :
2017 2018 | x | = | - | 4072323 2018 |
The coefficient of the unknown number is reduced to 1 :
| x | = | - | 4072323 2018 | ÷ | 2017 2018 |
| = | - | 4072323 2018 | × | 2018 2017 |
| = | - | 4072323 1009 | × | 1009 2017 |
We obtained :
| x | = | - | 4108973907 2035153 |
By reducing fraction, we can get:
| x | = | - | 4072323 2017 |
Convert the result to decimal form :
| x | = | - 2019 |