总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 100x+10(x+1)+3(x+1)-2+100[3(x+1)-2]+10(x+1)+x = 1171 的解.
题型:方程
解:原方程:| | 100 | x | + | 10 | ( | x | + | 1 | ) | + | 3 | ( | x | + | 1 | ) | − | 2 | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 | ( | x | + | 1 | ) | + | x | = | 1171 |
| 方程左边 = | 101 | x | + | 10 | ( | x | + | 1 | ) | + | 3 | ( | x | + | 1 | ) | − | 2 | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 | ( | x | + | 1 | ) |
方程化为:
| | 101 | x | + | 10 | ( | x | + | 1 | ) | + | 3 | ( | x | + | 1 | ) | − | 2 | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 | ( | x | + | 1 | ) | = | 1171 |
去掉方程左边的括号:
| 方程左边 = | 101 | x | + | 10 | x | + | 10 | × | 1 | + | 3 | ( | x | + | 1 | ) | − | 2 | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 |
| = | 101 | x | + | 10 | x | + | 10 | + | 3 | ( | x | + | 1 | ) | − | 2 | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 | ( | x | + | 1 | ) |
| = | 111 | x | + | 8 | + | 3 | ( | x | + | 1 | ) | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 | ( | x | + | 1 | ) |
| = | 111 | x | + | 8 | + | 3 | x | + | 3 | × | 1 | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 | ( | x | + | 1 | ) |
| = | 111 | x | + | 8 | + | 3 | x | + | 3 | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 | ( | x | + | 1 | ) |
| = | 114 | x | + | 11 | + | 100 | ( | 3 | ( | x | + | 1 | ) | − | 2 | ) | + | 10 | ( | x | + | 1 | ) |
| = | 114 | x | + | 11 | + | 100 | × | 3 | ( | x | + | 1 | ) | − | 100 | × | 2 | + | 10 | ( | x | + | 1 | ) |
| = | 114 | x | + | 11 | + | 300 | ( | x | + | 1 | ) | − | 200 | + | 10 | ( | x | + | 1 | ) |
| = | 114 | x | − | 189 | + | 300 | ( | x | + | 1 | ) | + | 10 | ( | x | + | 1 | ) |
| = | 114 | x | − | 189 | + | 300 | x | + | 300 | × | 1 | + | 10 | ( | x | + | 1 | ) |
| = | 114 | x | − | 189 | + | 300 | x | + | 300 | + | 10 | ( | x | + | 1 | ) |
| = | 414 | x | + | 111 | + | 10 | ( | x | + | 1 | ) |
| = | 414 | x | + | 111 | + | 10 | x | + | 10 | × | 1 |
| = | 414 | x | + | 111 | + | 10 | x | + | 10 |
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。
合并方程右边的各项:
把未知数的系数化为 1:
得:
把结果化为小数形式:
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