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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 -149/16-11/3r = -7/4r-5/4(-4/3r+1) .
Question type: Equation
Solution:Original question:
| - | 149 | ÷ | 16 | − | 11 | ÷ | 3 | × | r | = | - | 7 | ÷ | 4 | × | r | − | 5 | ÷ | 4 | × | ( | - | 4 | ÷ | 3 | × | r | + | 1 | ) |
| Left side of the equation = | - | 149 16 | − | 11 3 | r |
| - | 149 16 | − | 11 3 | r | = | - | 7 | ÷ | 4 | × | r | − | 5 | ÷ | 4 | × | ( | - | 4 | ÷ | 3 | × | r | + | 1 | ) |
| Right side of the equation = | - | 7 4 | r | − | 5 4 | ( | - | 4 | ÷ | 3 | × | r | + | 1 | ) |
| - | 149 16 | − | 11 3 | r | = | - | 7 4 | r | − | 5 4 | ( | - | 4 | ÷ | 3 | × | r | + | 1 | ) |
| Right side of the equation = | - | 7 4 | r | + | 5 4 | × | 4 | ÷ | 3 | × | r | − | 5 4 | × | 1 |
| = | - | 7 4 | r | + | 5 3 | r | − | 5 4 |
| = | - | 1 12 | r | − | 5 4 |
| - | 149 16 | − | 11 3 | r | = | - | 1 12 | r | − | 5 4 |
Transposition :
| - | 11 3 | r | + | 1 12 | r | = | - | 5 4 | + | 149 16 |
Combine the items on the left of the equation:
| - | 43 12 | r | = | - | 5 4 | + | 149 16 |
Combine the items on the right of the equation:
| - | 43 12 | r | = | 129 16 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
| - | 129 16 | = | 43 12 | r |
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 :
43 12 | r | = | - | 129 16 |
The coefficient of the unknown number is reduced to 1 :
| r | = | - | 129 16 | ÷ | 43 12 |
| = | - | 129 16 | × | 12 43 |
| = | - | 3 4 | × | 3 |
We obtained :
| r | = | - | 9 4 |
Convert the result to decimal form :
| r | = | - 2.25 |