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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-23)/2+(x-19)/4+(x-15)/6+(x-11)/8+(x-7)/10 = 10 .
Question type: Equation
Solution:Original question:
| ( | x | − | 23 | ) | ÷ | 2 | + | ( | x | − | 19 | ) | ÷ | 4 | + | ( | x | − | 15 | ) | ÷ | 6 | + | ( | x | − | 11 | ) | ÷ | 8 | + | ( | x | − | 7 | ) | ÷ | 10 | = | 10 |
| Left side of the equation = | x | × | 1 2 | − | 23 | × | 1 2 | + | ( | x | − | 19 | ) | × | 1 4 | + | ( | x | − | 15 | ) | × | 1 6 | + | ( | x | − | 11 | ) | × | 1 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | x | × | 1 2 | − | 23 2 | + | ( | x | − | 19 | ) | × | 1 4 | + | ( | x | − | 15 | ) | × | 1 6 | + | ( | x | − | 11 | ) | × | 1 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 1 2 | x | − | 23 2 | + | x | × | 1 4 | − | 19 | × | 1 4 | + | ( | x | − | 15 | ) | × | 1 6 | + | ( | x | − | 11 | ) | × | 1 8 | + | ( | x | − | 7 | ) |
| = | 1 2 | x | − | 23 2 | + | x | × | 1 4 | − | 19 4 | + | ( | x | − | 15 | ) | × | 1 6 | + | ( | x | − | 11 | ) | × | 1 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 3 4 | x | − | 65 4 | + | ( | x | − | 15 | ) | × | 1 6 | + | ( | x | − | 11 | ) | × | 1 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 3 4 | x | − | 65 4 | + | x | × | 1 6 | − | 15 | × | 1 6 | + | ( | x | − | 11 | ) | × | 1 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 3 4 | x | − | 65 4 | + | x | × | 1 6 | − | 5 2 | + | ( | x | − | 11 | ) | × | 1 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 11 12 | x | − | 75 4 | + | ( | x | − | 11 | ) | × | 1 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 11 12 | x | − | 75 4 | + | x | × | 1 8 | − | 11 | × | 1 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 11 12 | x | − | 75 4 | + | x | × | 1 8 | − | 11 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 25 24 | x | − | 161 8 | + | ( | x | − | 7 | ) | × | 1 10 |
| = | 25 24 | x | − | 161 8 | + | x | × | 1 10 | − | 7 | × | 1 10 |
| = | 25 24 | x | − | 161 8 | + | x | × | 1 10 | − | 7 10 |
| = | 137 120 | x | − | 833 40 |
137 120 | x | − | 833 40 | = | 10 |
Transposition :
137 120 | x | = | 10 | + | 833 40 |
Combine the items on the right of the equation:
137 120 | x | = | 1233 40 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 1233 40 | ÷ | 137 120 |
| = | 1233 40 | × | 120 137 |
| = | 1233 | × | 3 137 |
We obtained :
| x | = | 3699 137 |
By reducing fraction, we can get:
| x | = | 27 |