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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 (2y-5)/2022-3 = (2y-5)*2022+(2022*2022-4) .
Question type: Equation
Solution:Original question:
| ( | 2 | y | − | 5 | ) | ÷ | 2022 | − | 3 | = | ( | 2 | y | − | 5 | ) | × | 2022 | + | ( | 2022 | × | 2022 | − | 4 | ) |
| Left side of the equation = | 2 | y | × | 1 2022 | − | 5 | × | 1 2022 | − | 3 |
| = | 1 1011 | y | − | 5 2022 | − | 3 |
| = | 1 1011 | y | − | 6071 2022 |
1 1011 | y | − | 6071 2022 | = | ( | 2 | y | − | 5 | ) | × | 2022 | + | ( | 2022 | × | 2022 | − | 4 | ) |
| Right side of the equation = | 2 | y | × | 2022 | − | 5 | × | 2022 | + | ( | 2022 | × | 2022 | − | 4 | ) |
| = | 4044 | y | − | 10110 | + | ( | 2022 | × | 2022 | − | 4 | ) |
| = | 4044 | y | − | 10110 | + | 2022 | × | 2022 | − | 4 |
| = | 4044 | y | − | 10110 | + | 4088484 | − | 4 |
| = | 4044 | y | + | 4078370 |
1 1011 | y | − | 6071 2022 | = | 4044 | y | + | 4078370 |
Transposition :
1 1011 | y | − | 4044 | y | = | 4078370 | + | 6071 2022 |
Combine the items on the left of the equation:
| - | 4088483 1011 | y | = | 4078370 | + | 6071 2022 |
Combine the items on the right of the equation:
| - | 4088483 1011 | y | = | 8246470211 2022 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
| - | 8246470211 2022 | = | 4088483 1011 | y |
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 :
4088483 1011 | y | = | - | 8246470211 2022 |
The coefficient of the unknown number is reduced to 1 :
| y | = | - | 8246470211 2022 | ÷ | 4088483 1011 |
| = | - | 8246470211 2022 | × | 1011 4088483 |
| = | - | 2017 674 | × | 337 |
We obtained :
| y | = | - | 679729 674 |
By reducing fraction, we can get:
| y | = | - | 2017 2 |
Convert the result to decimal form :
| y | = | - 1008.5 |