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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 （18870－18680）/（x－8.894） = （19200－18870）/（8.894－x） .
Question type: Equation
Solution:Original question:
Remove a bracket on the left of the equation:：
Remove a bracket on the right of the equation:：
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
The equation is reduced to :
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
The equation is reduced to :
The equation is reduced to :
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 :
However,when simplifying the equation, multiply both sides by ( x − ) , and when
, its value is 0. Therefore, the value of this unknown number is not the solution of the equation, and the input to the equation is incorrect.
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation （18870－18680）/（x－8.894） = （19200－18870）/（8.894－x） .
Question type: Equation
Solution:Original question:
| ( | 18870 | − | 18680 | ) | ÷ | ( | x | − | 4447 500 | ) | = | ( | 19200 | − | 18870 | ) | ÷ | ( | 4447 500 | − | x | ) |
| Multiply both sides of the equation by: | ( | x | − | 4447 500 | ) | , | ( | 4447 500 | − | x | ) |
| ( | 18870 | − | 18680 | ) | ( | 4447 500 | − | x | ) | = | ( | 19200 | − | 18870 | ) | ( | x | − | 4447 500 | ) |
| 18870 | ( | 4447 500 | − | x | ) | − | 18680 | ( | 4447 500 | − | x | ) | = | ( | 19200 | − | 18870 | ) | ( | x | − | 4447 500 | ) |
| 18870 | ( | 4447 500 | − | x | ) | − | 18680 | ( | 4447 500 | − | x | ) | = | 19200 | ( | x | − | 4447 500 | ) | − | 18870 | ( | x | − | 4447 500 | ) |
| 18870 | × | 4447 500 | − | 18870 | x | − | 18680 | ( | 4447 500 | − | x | ) | = | 19200 | ( | x | − | 4447 500 | ) | − | 18870 | ( | x | − | 4447 500 | ) |
| 18870 | × | 4447 500 | − | 18870 | x | − | 18680 | ( | 4447 500 | − | x | ) | = | 19200 | x | − | 19200 | × | 4447 500 | − | 18870 | ( | x | − | 4447 500 | ) |
8391489 50 | − | 18870 | x | − | 18680 | ( | 4447 500 | − | x | ) | = | 19200 | x | − | 853824 5 | − | 18870 | ( | x | − | 4447 500 | ) |
8391489 50 | − | 18870 | x | − | 18680 | × | 4447 500 | + | 18680 | x | = | 19200 | x | − | 853824 5 | − | 18870 | ( | x | − | 4447 500 | ) |
8391489 50 | − | 18870 | x | − | 18680 | × | 4447 500 | + | 18680 | x | = | 19200 | x | − | 853824 5 | − | 18870 | x | + | 18870 | × | 4447 500 |
8391489 50 | − | 18870 | x | − | 4153498 25 | + | 18680 | x | = | 19200 | x | − | 853824 5 | − | 18870 | x | + | 8391489 50 |
84493 50 | − | 190 | x | = | 330 | x | − | 146751 50 |
Transposition :
| - | 190 | x | − | 330 | x | = | - | 146751 50 | − | 84493 50 |
Combine the items on the left of the equation:
| - | 520 | x | = | - | 146751 50 | − | 84493 50 |
Combine the items on the right of the equation:
| - | 520 | x | = | - | 115622 25 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
115622 25 | = | 520 | 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 :
| 520 | x | = | 115622 25 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 115622 25 | ÷ | 520 |
| = | 115622 25 | × | 1 520 |
| = | 4447 25 | × | 1 20 |
We obtained :
| x | = | 4447 500 |
4447
500
| x | = | 4447 500 |