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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－42）÷（13÷25） = （3÷5）x÷（13÷25） .
Question type: Equation
Solution:Original question:
| ( | x | − | 42 | ) | ÷ | ( | 13 | ÷ | 25 | ) | = | ( | 3 | ÷ | 5 | ) | x | ÷ | ( | 13 | ÷ | 25 | ) |
| Multiply both sides of the equation by: | ( | 13 | ÷ | 25 | ) | , | ( | 13 | ÷ | 25 | ) |
| ( | x | − | 42 | ) | ( | 13 | ÷ | 25 | ) | = | ( | 3 | ÷ | 5 | ) | x | ( | 13 | ÷ | 25 | ) |
| x | ( | 13 | ÷ | 25 | ) | − | 42 | ( | 13 | ÷ | 25 | ) | = | ( | 3 | ÷ | 5 | ) | x | ( | 13 | ÷ | 25 | ) |
| x | ( | 13 | ÷ | 25 | ) | − | 42 | ( | 13 | ÷ | 25 | ) | = | 3 | ÷ | 5 | × | x | ( | 13 | ÷ | 25 | ) |
| x | ( | 13 | ÷ | 25 | ) | − | 42 | ( | 13 | ÷ | 25 | ) | = | 3 5 | x | ( | 13 | ÷ | 25 | ) |
| x | × | 13 | ÷ | 25 | − | 42 | ( | 13 | ÷ | 25 | ) | = | 3 5 | x | ( | 13 | ÷ | 25 | ) |
| x | × | 13 | ÷ | 25 | − | 42 | ( | 13 | ÷ | 25 | ) | = | 3 5 | x | × | 13 | ÷ | 25 |
| x | × | 13 25 | − | 42 | ( | 13 | ÷ | 25 | ) | = | 39 125 | x |
13 25 | x | − | 42 | × | 13 | ÷ | 25 | = | 39 125 | x |
13 25 | x | − | 546 25 | = | 39 125 | x |
Transposition :
13 25 | x | − | 39 125 | x | = | 546 25 |
Combine the items on the left of the equation:
26 125 | x | = | 546 25 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 546 25 | ÷ | 26 125 |
| = | 546 25 | × | 125 26 |
| = | 21 | × | 5 |
We obtained :
| x | = | 105 |