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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-500）*0.75/400 = （x-500）*0.75-102/300 .
Question type: Equation
Solution:Original question:
| ( | x | − | 500 | ) | × | 3 4 | ÷ | 400 | = | ( | x | − | 500 | ) | × | 3 4 | − | 102 | ÷ | 300 |
| Left side of the equation = | ( | x | − | 500 | ) | × | 3 1600 |
| ( | x | − | 500 | ) | × | 3 1600 | = | ( | x | − | 500 | ) | × | 3 4 | − | 102 | ÷ | 300 |
| Left side of the equation = | x | × | 3 1600 | − | 500 | × | 3 1600 |
| = | x | × | 3 1600 | − | 15 16 |
3 1600 | x | − | 15 16 | = | ( | x | − | 500 | ) | × | 3 4 | − | 102 | ÷ | 300 |
| Right side of the equation = | ( | x | − | 500 | ) | × | 3 4 | − | 17 50 |
3 1600 | x | − | 15 16 | = | ( | x | − | 500 | ) | × | 3 4 | − | 17 50 |
| Right side of the equation = | x | × | 3 4 | − | 500 | × | 3 4 | − | 17 50 |
| = | x | × | 3 4 | − | 375 | − | 17 50 |
| = | 3 4 | x | − | 18767 50 |
3 1600 | x | − | 15 16 | = | 3 4 | x | − | 18767 50 |
Transposition :
3 1600 | x | − | 3 4 | x | = | - | 18767 50 | + | 15 16 |
Combine the items on the left of the equation:
| - | 1197 1600 | x | = | - | 18767 50 | + | 15 16 |
Combine the items on the right of the equation:
| - | 1197 1600 | x | = | - | 149761 400 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
149761 400 | = | 1197 1600 | 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 :
1197 1600 | x | = | 149761 400 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 149761 400 | ÷ | 1197 1600 |
| = | 149761 400 | × | 1600 1197 |
| = | 149761 | × | 4 1197 |
We obtained :
| x | = | 599044 1197 |
Convert the result to decimal form :
| x | = | 500.45447 |