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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 2022/2023*(2y-1)+5 = 7*(2y-1)+35+5/2023 .
Question type: Equation
Solution:Original question:
The equation is transformed into :
Remove the bracket on the left of the equation:
The equation is transformed into :
The equation is transformed into :
Remove the bracket on the right of the equation:
The equation is transformed into :
Transposition :
Combine the items on the left of the equation:
Combine the items on the right of the equation:
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
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 :
The coefficient of the unknown number is reduced to 1 :
We obtained :
This is the solution of the equation.
By reducing fraction, we can get:
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation 2022/2023*(2y-1)+5 = 7*(2y-1)+35+5/2023 .
Question type: Equation
Solution:Original question:
| 2022 | ÷ | 2023 | × | ( | 2 | y | − | 1 | ) | + | 5 | = | 7 | ( | 2 | y | − | 1 | ) | + | 35 | + | 5 | ÷ | 2023 |
| Left side of the equation = | 2022 2023 | ( | 2 | y | − | 1 | ) | + | 5 |
2022 2023 | ( | 2 | y | − | 1 | ) | + | 5 | = | 7 | ( | 2 | y | − | 1 | ) | + | 35 | + | 5 | ÷ | 2023 |
| Left side of the equation = | 2022 2023 | × | 2 | y | − | 2022 2023 | × | 1 | + | 5 |
| = | 4044 2023 | y | − | 2022 2023 | + | 5 |
| = | 4044 2023 | y | + | 8093 2023 |
4044 2023 | y | + | 8093 2023 | = | 7 | ( | 2 | y | − | 1 | ) | + | 35 | + | 5 | ÷ | 2023 |
| Right side of the equation = | 7 | ( | 2 | y | − | 1 | ) | + | 35 | + | 5 2023 |
| = | 7 | ( | 2 | y | − | 1 | ) | + | 70810 2023 |
4044 2023 | y | + | 8093 2023 | = | 7 | ( | 2 | y | − | 1 | ) | + | 70810 2023 |
| Right side of the equation = | 7 | × | 2 | y | − | 7 | × | 1 | + | 70810 2023 |
| = | 14 | y | − | 7 | + | 70810 2023 |
| = | 14 | y | + | 56649 2023 |
4044 2023 | y | + | 8093 2023 | = | 14 | y | + | 56649 2023 |
Transposition :
4044 2023 | y | − | 14 | y | = | 56649 2023 | − | 8093 2023 |
Combine the items on the left of the equation:
| - | 24278 2023 | y | = | 56649 2023 | − | 8093 2023 |
Combine the items on the right of the equation:
| - | 24278 2023 | y | = | 48556 2023 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
| - | 48556 2023 | = | 24278 2023 | 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 :
24278 2023 | y | = | - | 48556 2023 |
The coefficient of the unknown number is reduced to 1 :
| y | = | - | 48556 2023 | ÷ | 24278 2023 |
| = | - | 48556 2023 | × | 2023 24278 |
| = | - | 398 | × | 1 199 |
We obtained :
| y | = | - | 398 199 |
By reducing fraction, we can get:
| y | = | - | 2 |