| ( | 1 | + | 1 2 | ) | x | ÷ | 2 | + | ( | 1 | + | 2 5 | ) | ( | 500 | − | x | ) | × | 9 10 | = | 120 |
| 方程左边 = | 1 | x | × | 1 2 | + | 1 2 | x | × | 1 2 | + | ( | 1 | + | 2 5 | ) | ( | 500 | − | x | ) | × | 9 10 |
| = | 1 2 | x | + | 1 4 | x | + | ( | 1 | + | 2 5 | ) | ( | 500 | − | x | ) | × | 9 10 |
| = | 3 4 | x | + | ( | 1 | + | 2 5 | ) | ( | 500 | − | x | ) | × | 9 10 |
| = | 3 4 | x | + | 1 | ( | 500 | − | x | ) | × | 9 10 | + | 2 5 | ( | 500 | − | x | ) | × | 9 10 |
| = | 3 4 | x | + | 9 10 | ( | 500 | − | x | ) | + | 9 25 | ( | 500 | − | x | ) |
| = | 3 4 | x | + | 9 10 | × | 500 | − | 9 10 | x | + | 9 25 | ( | 500 | − | x | ) |
| = | 3 4 | x | + | 450 | − | 9 10 | x | + | 9 25 | ( | 500 | − | x | ) |
| = | - | 3 20 | x | + | 450 | + | 9 25 | ( | 500 | − | x | ) |
| = | - | 3 20 | x | + | 450 | + | 9 25 | × | 500 | − | 9 25 | x |
| = | - | 3 20 | x | + | 450 | + | 180 | − | 9 25 | x |
| = | - | 51 100 | x | + | 630 |
| - | 51 100 | x | + | 630 | = | 120 |
| - | 51 100 | x | = | 120 | − | 630 |
| - | 51 100 | x | = | - | 510 |
| 510 | = | 51 100 | x |
51 100 | x | = | 510 |
| x | = | 510 | ÷ | 51 100 |
| = | 510 | × | 100 51 |
| = | 10 | × | 100 |
| x | = | 1000 |