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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 (x-300)/((300/42600)*x) = (x-1000)/((1000/42600)*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:：
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 :
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
The equation is reduced to :
Transposition :
Combine the items on the left of the equation:
Combine the items on the right of the equation:
The coefficient of the unknown number is reduced to 1 :
We obtained :
However,when simplifying the equation, multiply both sides by ( ( 300 ÷ 42600 ) 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 (x-300)/((300/42600)*x) = (x-1000)/((1000/42600)*x) .
Question type: Equation
Solution:Original question:
| ( | x | − | 300 | ) | ÷ | ( | ( | 300 | ÷ | 42600 | ) | x | ) | = | ( | x | − | 1000 | ) | ÷ | ( | ( | 1000 | ÷ | 42600 | ) | x | ) |
| Multiply both sides of the equation by: | ( | ( | 300 | ÷ | 42600 | ) | x | ) | , | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) |
| ( | x | − | 300 | ) | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | = | ( | x | − | 1000 | ) | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
| x | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | − | 300 | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | = | ( | x | − | 1000 | ) | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
| x | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | − | 300 | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | = | x | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) | − | 1000 | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
| x | ( | 1000 | ÷ | 42600 | ) | × | 1 | − | 300 | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | = | x | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) | − | 1000 | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
| x | ( | 1000 | ÷ | 42600 | ) | × | 1 | − | 300 | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | = | x | ( | 300 | ÷ | 42600 | ) | × | 1 | − | 1000 | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
| x | × | 1000 | ÷ | 42600 | × | 1 | − | 300 | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | = | x | ( | 300 | ÷ | 42600 | ) | × | 1 | − | 1000 | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
| x | × | 1000 | ÷ | 42600 | × | 1 | − | 300 | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | = | x | × | 300 | ÷ | 42600 | × | 1 | − | 1000 | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
| x | × | 5 213 | − | 300 | ( | ( | 1000 | ÷ | 42600 | ) | × | 1 | ) | = | x | × | 1 142 | − | 1000 | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
5 213 | x | − | 300 | ( | 1000 | ÷ | 42600 | ) | × | 1 | = | 1 142 | x | − | 1000 | ( | ( | 300 | ÷ | 42600 | ) | × | 1 | ) |
5 213 | x | − | 300 | ( | 1000 | ÷ | 42600 | ) | × | 1 | = | 1 142 | x | − | 1000 | ( | 300 | ÷ | 42600 | ) | × | 1 |
5 213 | x | − | 300 | ( | 1000 | ÷ | 42600 | ) | = | 1 142 | x | − | 1000 | ( | 300 | ÷ | 42600 | ) |
5 213 | x | − | 300 | × | 1000 | ÷ | 42600 | = | 1 142 | x | − | 1000 | ( | 300 | ÷ | 42600 | ) |
5 213 | x | − | 300 | × | 1000 | ÷ | 42600 | = | 1 142 | x | − | 1000 | × | 300 | ÷ | 42600 |
5 213 | x | − | 500 71 | = | 1 142 | x | − | 500 71 |
Transposition :
5 213 | x | − | 1 142 | x | = | - | 500 71 | + | 500 71 |
Combine the items on the left of the equation:
7 426 | x | = | - | 500 71 | + | 500 71 |
Combine the items on the right of the equation:
7 426 | x | = | - | 0 |
The coefficient of the unknown number is reduced to 1 :
| x | = | - | 0 | ÷ | 7 426 |
| = | - | 0 | × | 426 7 |
| = | - | 0 | × | 6 7 |
We obtained :
| x | = | 0 |
| x | = | 0 |