[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.23,0:00:04.28,Default,,0000,0000,0000,,欢迎来到线性方程第四课
Dialogue: 0,0:00:04.28,0:00:06.54,Default,,0000,0000,0000,,让我们来解题吧
Dialogue: 0,0:00:06.54,0:00:06.71,Default,,0000,0000,0000,,首先
Dialogue: 0,0:00:06.71,0:00:09.58,Default,,0000,0000,0000,,假设我有一个情况——让我出几题
Dialogue: 0,0:00:09.58,0:00:20.11,Default,,0000,0000,0000,,——假设我有3/x等于5
Dialogue: 0,0:00:20.11,0:00:23.18,Default,,0000,0000,0000,,我们想要——这道题和我们以前见过的
Dialogue: 0,0:00:23.18,0:00:24.26,Default,,0000,0000,0000,,题目都不太一样
Dialogue: 0,0:00:24.26,0:00:26.95,Default,,0000,0000,0000,,因为不是在分子上有x
Dialogue: 0,0:00:26.95,0:00:28.15,Default,,0000,0000,0000,,我们现在是分母是x
Dialogue: 0,0:00:28.15,0:00:31.27,Default,,0000,0000,0000,,我自己不太喜欢分母含有x的情况
Dialogue: 0,0:00:31.27,0:00:34.19,Default,,0000,0000,0000,,所以我们想尽快将其
Dialogue: 0,0:00:34.19,0:00:36.14,Default,,0000,0000,0000,,从分母上拿出来，或者至少
Dialogue: 0,0:00:36.14,0:00:36.92,Default,,0000,0000,0000,,去除它
Dialogue: 0,0:00:36.92,0:00:40.78,Default,,0000,0000,0000,,一个将分母上的数提出来的方法是
Dialogue: 0,0:00:40.78,0:00:45.56,Default,,0000,0000,0000,,我们可以等式两侧同乘x
Dialogue: 0,0:00:45.56,0:00:47.46,Default,,0000,0000,0000,,左侧等式的两个x
Dialogue: 0,0:00:47.46,0:00:48.90,Default,,0000,0000,0000,,会相互抵消
Dialogue: 0,0:00:48.90,0:00:52.16,Default,,0000,0000,0000,,在右侧，你会得到5乘x
Dialogue: 0,0:00:52.16,0:00:56.92,Default,,0000,0000,0000,,这等于——两个x抵消掉
Dialogue: 0,0:00:56.92,0:01:00.89,Default,,0000,0000,0000,,你得到3等于5x
Dialogue: 0,0:01:00.89,0:01:05.42,Default,,0000,0000,0000,,现在，我们也可以将其写成5x等于3
Dialogue: 0,0:01:05.42,0:01:07.81,Default,,0000,0000,0000,,然后我们有两种思考方法
Dialogue: 0,0:01:07.81,0:01:12.21,Default,,0000,0000,0000,,我们可以两侧同时乘以1/5，或者你可以
Dialogue: 0,0:01:12.21,0:01:14.23,Default,,0000,0000,0000,,同除以5
Dialogue: 0,0:01:14.23,0:01:16.49,Default,,0000,0000,0000,,如果你两侧同乘以1/5
Dialogue: 0,0:01:16.49,0:01:18.68,Default,,0000,0000,0000,,左手边变成x
Dialogue: 0,0:01:18.68,0:01:23.74,Default,,0000,0000,0000,,右手边是3乘以1/5，等于3/5
Dialogue: 0,0:01:23.74,0:01:24.64,Default,,0000,0000,0000,,我们这做了什么？
Dialogue: 0,0:01:24.64,0:01:26.86,Default,,0000,0000,0000,,这就很快变成第二节课
Dialogue: 0,0:01:26.86,0:01:28.67,Default,,0000,0000,0000,,的题目，或者第一节课
Dialogue: 0,0:01:28.67,0:01:29.48,Default,,0000,0000,0000,,的题目
Dialogue: 0,0:01:29.48,0:01:31.99,Default,,0000,0000,0000,,我们只需要两侧同时
Dialogue: 0,0:01:31.99,0:01:33.26,Default,,0000,0000,0000,,乘以x
Dialogue: 0,0:01:33.26,0:01:35.46,Default,,0000,0000,0000,,我们就把x从分母上去除了
Dialogue: 0,0:01:35.46,0:01:36.36,Default,,0000,0000,0000,,我们再做一题
Dialogue: 0,0:01:41.11,0:01:53.53,Default,,0000,0000,0000,,假设我们有x加2除以x加1
Dialogue: 0,0:01:53.53,0:01:58.80,Default,,0000,0000,0000,,等于7
Dialogue: 0,0:01:58.80,0:02:00.79,Default,,0000,0000,0000,,这里的分母上不是只有x
Dialogue: 0,0:02:00.79,0:02:02.92,Default,,0000,0000,0000,,分母时x加1
Dialogue: 0,0:02:02.92,0:02:05.00,Default,,0000,0000,0000,,但我们的步骤一样
Dialogue: 0,0:02:05.00,0:02:09.17,Default,,0000,0000,0000,,要把x+1从分母上拿出来，我们可以
Dialogue: 0,0:02:09.17,0:02:15.45,Default,,0000,0000,0000,,灯饰两侧同时乘以x+1除以1
Dialogue: 0,0:02:15.45,0:02:17.01,Default,,0000,0000,0000,,既然我们左侧已经乘了
Dialogue: 0,0:02:17.01,0:02:19.64,Default,,0000,0000,0000,,右侧也得这样，就是7/1
Dialogue: 0,0:02:19.64,0:02:24.42,Default,,0000,0000,0000,,乘以x+1除以1
Dialogue: 0,0:02:24.42,0:02:27.72,Default,,0000,0000,0000,,左侧，x+1抵消
Dialogue: 0,0:02:27.72,0:02:31.11,Default,,0000,0000,0000,,只留下x+2
Dialogue: 0,0:02:31.11,0:02:33.30,Default,,0000,0000,0000,,除以1，但你可以忽略这个1
Dialogue: 0,0:02:33.30,0:02:39.26,Default,,0000,0000,0000,,这等于7乘以x+1
Dialogue: 0,0:02:39.26,0:02:41.93,Default,,0000,0000,0000,,这等于x+2
Dialogue: 0,0:02:41.93,0:02:45.72,Default,,0000,0000,0000,,记住，这是7乘以整个x+1
Dialogue: 0,0:02:45.72,0:02:47.79,Default,,0000,0000,0000,,所以我们得使用分配法则
Dialogue: 0,0:02:47.79,0:02:54.40,Default,,0000,0000,0000,,这等于7x加7
Dialogue: 0,0:02:54.40,0:02:57.20,Default,,0000,0000,0000,,现在，我们变成了一个
Dialogue: 0,0:02:57.20,0:02:58.79,Default,,0000,0000,0000,,三级方程
Dialogue: 0,0:02:58.79,0:03:02.05,Default,,0000,0000,0000,,我们现在要把所有x项
Dialogue: 0,0:03:02.05,0:03:02.96,Default,,0000,0000,0000,,放到等式左侧
Dialogue: 0,0:03:02.96,0:03:05.57,Default,,0000,0000,0000,,所有常数项，类似2和7，
Dialogue: 0,0:03:05.57,0:03:07.10,Default,,0000,0000,0000,,移到等式右侧
Dialogue: 0,0:03:07.10,0:03:08.89,Default,,0000,0000,0000,,我们首先把x移到左侧
Dialogue: 0,0:03:08.89,0:03:10.99,Default,,0000,0000,0000,,要把7x放到左侧
Dialogue: 0,0:03:10.99,0:03:14.45,Default,,0000,0000,0000,,我们可以两侧同时减7x
Dialogue: 0,0:03:14.45,0:03:19.44,Default,,0000,0000,0000,,负7x，加，这是负7x
Dialogue: 0,0:03:19.44,0:03:22.80,Default,,0000,0000,0000,,右手边，两个7x抵消
Dialogue: 0,0:03:22.80,0:03:26.41,Default,,0000,0000,0000,,左手边就时负7x加x
Dialogue: 0,0:03:26.41,0:03:32.84,Default,,0000,0000,0000,,就是负6x加2等于
Dialogue: 0,0:03:32.84,0:03:35.08,Default,,0000,0000,0000,,右侧剩下的7
Dialogue: 0,0:03:35.08,0:03:36.47,Default,,0000,0000,0000,,现在我们需要去掉2
Dialogue: 0,0:03:36.47,0:03:41.36,Default,,0000,0000,0000,,我们可以两侧同时减2
Dialogue: 0,0:03:41.36,0:03:48.00,Default,,0000,0000,0000,,剩下来的就是负6x等于5
Dialogue: 0,0:03:48.00,0:03:49.22,Default,,0000,0000,0000,,这是一级问题
Dialogue: 0,0:03:49.22,0:03:52.41,Default,,0000,0000,0000,,我们只需要两侧同时乘以
Dialogue: 0,0:03:52.41,0:03:54.20,Default,,0000,0000,0000,,左侧的因数的倒数
Dialogue: 0,0:03:54.20,0:03:56.15,Default,,0000,0000,0000,,因数是负6
Dialogue: 0,0:03:56.15,0:03:59.62,Default,,0000,0000,0000,,所以我们两侧同乘以负1/6
Dialogue: 0,0:04:02.54,0:04:05.61,Default,,0000,0000,0000,,负1/6
Dialogue: 0,0:04:05.61,0:04:08.89,Default,,0000,0000,0000,,左手边是负1/6乘以负6
Dialogue: 0,0:04:08.89,0:04:10.19,Default,,0000,0000,0000,,也就是1
Dialogue: 0,0:04:10.19,0:04:16.13,Default,,0000,0000,0000,,所以我们得到x等于5乘以负1/6
Dialogue: 0,0:04:16.13,0:04:19.25,Default,,0000,0000,0000,,就是负5/6
Dialogue: 0,0:04:22.27,0:04:23.21,Default,,0000,0000,0000,,题目结束
Dialogue: 0,0:04:23.21,0:04:25.71,Default,,0000,0000,0000,,如果你想要验算，你可以把
Dialogue: 0,0:04:25.71,0:04:28.95,Default,,0000,0000,0000,,x等于负5/6带回到原方程
Dialogue: 0,0:04:28.95,0:04:30.58,Default,,0000,0000,0000,,去检查一下是否成立
Dialogue: 0,0:04:30.58,0:04:31.34,Default,,0000,0000,0000,,让我们再做一题
Dialogue: 0,0:04:34.61,0:04:37.94,Default,,0000,0000,0000,,我临时想的题目，不好意思
Dialogue: 0,0:04:37.94,0:04:40.02,Default,,0000,0000,0000,,让我想想
Dialogue: 0,0:04:40.02,0:04:51.01,Default,,0000,0000,0000,,3乘以x加5等于8乘以x加2
Dialogue: 0,0:04:51.01,0:04:52.74,Default,,0000,0000,0000,,我们干同样的事
Dialogue: 0,0:04:52.74,0:04:55.95,Default,,0000,0000,0000,,虽然我们现在分母上有两个表达式
Dialogue: 0,0:04:55.95,0:04:56.68,Default,,0000,0000,0000,,我们都想提取出来
Dialogue: 0,0:04:56.68,0:04:58.87,Default,,0000,0000,0000,,我们想要把x+5提出来，我们想要
Dialogue: 0,0:04:58.87,0:05:00.01,Default,,0000,0000,0000,,把这个x+2也提出来
Dialogue: 0,0:05:00.01,0:05:01.67,Default,,0000,0000,0000,,首先做一下x+5
Dialogue: 0,0:05:01.67,0:05:03.64,Default,,0000,0000,0000,,就和之前一样，我们两侧同时
Dialogue: 0,0:05:03.64,0:05:05.57,Default,,0000,0000,0000,,乘以x+5
Dialogue: 0,0:05:05.57,0:05:07.63,Default,,0000,0000,0000,,你可以看成x+5除以1
Dialogue: 0,0:05:07.63,0:05:12.68,Default,,0000,0000,0000,,乘以x+5除以1
Dialogue: 0,0:05:12.68,0:05:15.08,Default,,0000,0000,0000,,在左侧，它们互相抵消
Dialogue: 0,0:05:15.08,0:05:24.23,Default,,0000,0000,0000,,剩下来的是3乘以8乘以x+5
Dialogue: 0,0:05:24.23,0:05:28.77,Default,,0000,0000,0000,,这个这个除以x+2
Dialogue: 0,0:05:28.77,0:05:31.82,Default,,0000,0000,0000,,现在，简化上面，
Dialogue: 0,0:05:31.82,0:05:34.42,Default,,0000,0000,0000,,我们只需要把8乘以整个表达式
Dialogue: 0,0:05:34.42,0:05:41.86,Default,,0000,0000,0000,,也就是8x加40除以x+2
Dialogue: 0,0:05:41.86,0:05:43.50,Default,,0000,0000,0000,,现在，我们去掉这个x+2
Dialogue: 0,0:05:43.50,0:05:44.51,Default,,0000,0000,0000,,我们用一样的方法
Dialogue: 0,0:05:44.51,0:05:46.50,Default,,0000,0000,0000,,我们两侧同时乘以
Dialogue: 0,0:05:46.50,0:05:50.90,Default,,0000,0000,0000,,x+2出1
Dialogue: 0,0:05:50.90,0:05:52.58,Default,,0000,0000,0000,,x+2
Dialogue: 0,0:05:52.58,0:05:53.69,Default,,0000,0000,0000,,我们可以看成两侧同乘
Dialogue: 0,0:05:53.69,0:05:54.42,Default,,0000,0000,0000,,x+2
Dialogue: 0,0:05:54.42,0:05:56.63,Default,,0000,0000,0000,,1是非必要的
Dialogue: 0,0:05:56.63,0:06:02.91,Default,,0000,0000,0000,,所以左侧变成3x加6
Dialogue: 0,0:06:02.91,0:06:05.07,Default,,0000,0000,0000,,记住，要把3分配进去，因为
Dialogue: 0,0:06:05.07,0:06:07.03,Default,,0000,0000,0000,,你是乘整个表达式
Dialogue: 0,0:06:07.03,0:06:08.54,Default,,0000,0000,0000,,x+2
Dialogue: 0,0:06:08.54,0:06:09.86,Default,,0000,0000,0000,,在右侧
Dialogue: 0,0:06:09.86,0:06:13.62,Default,,0000,0000,0000,,我们有x+2，和这个x+2相互抵消
Dialogue: 0,0:06:13.62,0:06:16.38,Default,,0000,0000,0000,,剩下来8x加40
Dialogue: 0,0:06:16.38,0:06:19.34,Default,,0000,0000,0000,,现在变成了三级问题
Dialogue: 0,0:06:19.34,0:06:25.38,Default,,0000,0000,0000,,如果我们两侧同减去8x，减8x，加——
Dialogue: 0,0:06:25.38,0:06:26.97,Default,,0000,0000,0000,,我觉得我没空间了
Dialogue: 0,0:06:26.97,0:06:28.47,Default,,0000,0000,0000,,减8x
Dialogue: 0,0:06:28.47,0:06:31.29,Default,,0000,0000,0000,,右侧的8x互相抵消
Dialogue: 0,0:06:31.29,0:06:38.62,Default,,0000,0000,0000,,左边我们有负5x加6等于
Dialogue: 0,0:06:38.62,0:06:42.32,Default,,0000,0000,0000,,右侧剩下的40
Dialogue: 0,0:06:42.32,0:06:45.38,Default,,0000,0000,0000,,现在我们可以等式两侧同减去6
Dialogue: 0,0:06:45.38,0:06:46.38,Default,,0000,0000,0000,,让我写出来
Dialogue: 0,0:06:46.38,0:06:49.51,Default,,0000,0000,0000,,减6x加负6
Dialogue: 0,0:06:49.51,0:06:51.47,Default,,0000,0000,0000,,现在，希望我没有太快
Dialogue: 0,0:06:51.47,0:06:53.16,Default,,0000,0000,0000,,你们可以跟上
Dialogue: 0,0:06:55.72,0:06:58.41,Default,,0000,0000,0000,,但如果我们两侧减去负6，在左边
Dialogue: 0,0:06:58.41,0:07:05.28,Default,,0000,0000,0000,,我们只剩下了负5x等于，
Dialogue: 0,0:07:05.28,0:07:08.78,Default,,0000,0000,0000,,在右边，我们有34
Dialogue: 0,0:07:08.78,0:07:09.88,Default,,0000,0000,0000,,现在变成了一级问题
Dialogue: 0,0:07:09.88,0:07:12.78,Default,,0000,0000,0000,,我们只需要两侧同时乘以负1/5
Dialogue: 0,0:07:16.51,0:07:18.36,Default,,0000,0000,0000,,负1/5
Dialogue: 0,0:07:18.36,0:07:21.13,Default,,0000,0000,0000,,在左边我们有x
Dialogue: 0,0:07:21.13,0:07:27.13,Default,,0000,0000,0000,,在右边我们有负34/5
Dialogue: 0,0:07:27.13,0:07:29.64,Default,,0000,0000,0000,,除非我大意出错，应该是对的
Dialogue: 0,0:07:29.64,0:07:33.19,Default,,0000,0000,0000,,我觉得你应该理解了我们这里的过程
Dialogue: 0,0:07:33.19,0:07:36.78,Default,,0000,0000,0000,,你现在应该准备好了解四级线性方程
Dialogue: 0,0:07:36.78,0:07:38.29,Default,,0000,0000,0000,,祝你好运