总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 1145567 = 1584x+(x-620)*1*12+(x+100-758)*1*5+(x-675)*4*5+(x-660)*1*6+(x-660)*3*5+(x+100-660)*1*5 的解.
题型:方程
解:原方程:| | 1145567 | = | 1584 | x | + | ( | x | − | 620 | ) | × | 1 | × | 12 | + | ( | x | + | 100 | − | 758 | ) | × | 1 | × | 5 | + | ( | x | − | 675 | ) | × | 4 | × | 5 | + | ( | x | − | 660 | ) |
| 方程右边 = | 1584 | x | + | ( | x | − | 620 | ) | × | 12 | + | ( | x | + | 100 | − | 758 | ) | × | 5 | + | ( | x | − | 675 | ) | × | 20 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) | × | 15 |
方程化为:
| | 1145567 | = | 1584 | x | + | ( | x | − | 620 | ) | × | 12 | + | ( | x | + | 100 | − | 758 | ) | × | 5 | + | ( | x | − | 675 | ) | × | 20 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) | × | 15 |
去掉方程右边的括号:
| 方程右边 = | 1584 | x | + | x | × | 12 | − | 620 | × | 12 | + | ( | x | + | 100 | − | 758 | ) | × | 5 | + | ( | x | − | 675 | ) | × | 20 | + | ( | x | − | 660 | ) | × | 6 |
| = | 1584 | x | + | x | × | 12 | − | 7440 | + | ( | x | + | 100 | − | 758 | ) | × | 5 | + | ( | x | − | 675 | ) | × | 20 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) |
| = | 1596 | x | − | 7440 | + | ( | x | + | 100 | − | 758 | ) | × | 5 | + | ( | x | − | 675 | ) | × | 20 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) | × | 15 | + | ( | x | + | 100 | − | 660 | ) |
| = | 1596 | x | − | 7440 | + | x | × | 5 | + | 100 | × | 5 | − | 758 | × | 5 | + | ( | x | − | 675 | ) | × | 20 | + | ( | x | − | 660 | ) |
| = | 1596 | x | − | 7440 | + | x | × | 5 | + | 500 | − | 3790 | + | ( | x | − | 675 | ) | × | 20 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) |
| = | 1601 | x | − | 10730 | + | ( | x | − | 675 | ) | × | 20 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) | × | 15 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1601 | x | − | 10730 | + | x | × | 20 | − | 675 | × | 20 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) | × | 15 | + | ( | x | + | 100 | − | 660 | ) |
| = | 1601 | x | − | 10730 | + | x | × | 20 | − | 13500 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) | × | 15 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1621 | x | − | 24230 | + | ( | x | − | 660 | ) | × | 6 | + | ( | x | − | 660 | ) | × | 15 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1621 | x | − | 24230 | + | x | × | 6 | − | 660 | × | 6 | + | ( | x | − | 660 | ) | × | 15 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1621 | x | − | 24230 | + | x | × | 6 | − | 3960 | + | ( | x | − | 660 | ) | × | 15 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1627 | x | − | 28190 | + | ( | x | − | 660 | ) | × | 15 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1627 | x | − | 28190 | + | x | × | 15 | − | 660 | × | 15 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1627 | x | − | 28190 | + | x | × | 15 | − | 9900 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1642 | x | − | 38090 | + | ( | x | + | 100 | − | 660 | ) | × | 5 |
| = | 1642 | x | − | 38090 | + | x | × | 5 | + | 100 | × | 5 | − | 660 | × | 5 |
| = | 1642 | x | − | 38090 | + | x | × | 5 | + | 500 | − | 3300 |
方程化为:
移项:即,把含有未知数的项移到方程左边,把只含有常数的项移到方程的右边。
注意,移项时,该项前面的正负号要改变,即,正号变为负号,而负号要改变为正号。这与方程两边同时加上或者减去该项是等价的。
| | - | 1647 | x | = | - | 40890 | − | 1145567 |
合并方程右边的各项:
方程两边同时移项,改变符号 得:
方程的左边等于右边,则右边也 一定等于左边,即:
把未知数的系数化为 1:
得:
把结果化为小数形式:
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