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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 40÷（（1÷（1/3））+（1÷（1/2）））÷（1/2） = x .
Question type: Equation
Solution:Original question:
Remove a bracket on the right 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 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 right of the equation:：
The equation is reduced to :
Remove a bracket on the right of the equation:：
The equation is reduced to :
The equation is reduced to :
Transposition :
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.
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation 40÷（（1÷（1/3））+（1÷（1/2）））÷（1/2） = x .
Question type: Equation
Solution:Original question:
| 40 | ÷ | ( | ( | 1 | ÷ | ( | 1 | ÷ | 3 | ) | ) | + | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ) | ÷ | ( | 1 | ÷ | 2 | ) | = | x |
| Multiply both sides of the equation by: | ( | ( | 1 | ÷ | ( | 1 | ÷ | 3 | ) | ) | + | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ) |
| 40 | ÷ | ( | 1 | ÷ | 2 | ) | = | x | ( | ( | 1 | ÷ | ( | 1 | ÷ | 3 | ) | ) | + | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ) |
| 40 | ÷ | ( | 1 | ÷ | 2 | ) | = | x | ( | 1 | ÷ | ( | 1 | ÷ | 3 | ) | ) | + | x | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) |
| Multiply both sides of the equation by: | ( | 1 | ÷ | 2 | ) |
| 40 | = | x | ( | 1 | ÷ | ( | 1 | ÷ | 3 | ) | ) | ( | 1 | ÷ | 2 | ) | + | x | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 1 | ÷ | 2 | ) |
| 40 | = | x | × | 1 | ÷ | ( | 1 | ÷ | 3 | ) | × | ( | 1 | ÷ | 2 | ) | + | x | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 1 | ÷ | 2 | ) |
| Multiply both sides of the equation by: | ( | 1 | ÷ | 3 | ) |
| 40 | ( | 1 | ÷ | 3 | ) | = | x | × | 1 | ( | 1 | ÷ | 2 | ) | + | x | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
| 40 | × | 1 | ÷ | 3 | = | x | × | 1 | ( | 1 | ÷ | 2 | ) | + | x | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
| 40 | × | 1 | ÷ | 3 | = | x | × | 1 | × | 1 | ÷ | 2 | + | x | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
40 3 | = | x | × | 1 2 | + | x | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
40 3 | = | 1 2 | x | + | x | × | 1 | ÷ | ( | 1 | ÷ | 2 | ) | × | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
| Multiply both sides of the equation by: | ( | 1 | ÷ | 2 | ) |
40 3 | ( | 1 | ÷ | 2 | ) | = | 1 2 | x | ( | 1 | ÷ | 2 | ) | + | x | × | 1 | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
40 3 | × | 1 | ÷ | 2 | = | 1 2 | x | ( | 1 | ÷ | 2 | ) | + | x | × | 1 | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
40 3 | × | 1 | ÷ | 2 | = | 1 2 | x | × | 1 | ÷ | 2 | + | x | × | 1 | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
20 3 | = | 1 4 | x | + | x | × | 1 | ( | 1 | ÷ | 2 | ) | ( | 1 | ÷ | 3 | ) |
20 3 | = | 1 4 | x | + | x | × | 1 | × | 1 | ÷ | 2 | × | ( | 1 | ÷ | 3 | ) |
20 3 | = | 1 4 | x | + | x | × | 1 2 | ( | 1 | ÷ | 3 | ) |
20 3 | = | 1 4 | x | + | x | × | 1 2 | × | 1 | ÷ | 3 |
20 3 | = | 1 4 | x | + | x | × | 1 6 |
20 3 | = | 5 12 | x |
Transposition :
| - | 5 12 | x | = | - | 20 3 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
20 3 | = | 5 12 | 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 :
5 12 | x | = | 20 3 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 20 3 | ÷ | 5 12 |
| = | 20 3 | × | 12 5 |
| = | 4 | × | 4 |
We obtained :
| x | = | 16 |