Equations
Unfold
Math OP
Fold
Linear algebra
Unfold
Mathematical calculation：
Enter the mathematical formula directly and click the "Next" button to get the calculation answer.
It supports mathematical functions (including trigonometric functions).
Enter the mathematical formula directly and click the "Next" button to get the calculation answer.
It supports mathematical functions (including trigonometric functions).
Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (x+1)＋2(x＋1)＋3(x＋1)＋4(x＋1) = 5(x＋1)+6(x-1) .
Question type: Equation
Solution:Original question:
Remove the bracket on the left of the equation:
The equation is transformed into :
Remove the bracket on the right of the equation:
The equation is transformed into :
Transposition :
i.e.
Combine the items on the left of the equation:
Combine the items on the right of the equation:
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 :
This is the solution of the equation.
This is the solution of the equation.
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (x+1)＋2(x＋1)＋3(x＋1)＋4(x＋1) = 5(x＋1)+6(x-1) .
Question type: Equation
Solution:Original question:
| ( | x | + | 1 | ) | + | 2 | ( | x | + | 1 | ) | + | 3 | ( | x | + | 1 | ) | + | 4 | ( | x | + | 1 | ) | = | 5 | ( | x | + | 1 | ) | + | 6 | ( | x | − | 1 | ) |
| Left side of the equation = | x | + | 1 | + | 2 | ( | x | + | 1 | ) | + | 3 | ( | x | + | 1 | ) | + | 4 | ( | x | + | 1 | ) |
| = | x | + | 1 | + | 2 | x | + | 2 | × | 1 | + | 3 | ( | x | + | 1 | ) | + | 4 | ( | x | + | 1 | ) |
| = | x | + | 1 | + | 2 | x | + | 2 | + | 3 | ( | x | + | 1 | ) | + | 4 | ( | x | + | 1 | ) |
| = | 3 | x | + | 3 | + | 3 | ( | x | + | 1 | ) | + | 4 | ( | x | + | 1 | ) |
| = | 3 | x | + | 3 | + | 3 | x | + | 3 | × | 1 | + | 4 | ( | x | + | 1 | ) |
| = | 3 | x | + | 3 | + | 3 | x | + | 3 | + | 4 | ( | x | + | 1 | ) |
| = | 6 | x | + | 6 | + | 4 | ( | x | + | 1 | ) |
| = | 6 | x | + | 6 | + | 4 | x | + | 4 | × | 1 |
| = | 6 | x | + | 6 | + | 4 | x | + | 4 |
| = | 10 | x | + | 10 |
| 10 | x | + | 10 | = | 5 | ( | x | + | 1 | ) | + | 6 | ( | x | − | 1 | ) |
| Right side of the equation = | 5 | x | + | 5 | × | 1 | + | 6 | ( | x | − | 1 | ) |
| = | 5 | x | + | 5 | + | 6 | ( | x | − | 1 | ) |
| = | 5 | x | + | 5 | + | 6 | x | − | 6 | × | 1 |
| = | 5 | x | + | 5 | + | 6 | x | − | 6 |
| = | 11 | x | − | 1 |
| 10 | x | + | 10 | = | 11 | x | − | 1 |
Transposition :
| 10 | x | − | 11 | x | = | - | 1 | − | 10 |
| - | x | = | - | 1 | − | 10 |
Combine the items on the left of the equation:
| - | x | = | - | 1 | − | 10 |
Combine the items on the right of the equation:
| - | x | = | - | 11 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
| 11 | = | 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 :
| x | = | 11 |
This is the solution of the equation.