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欢迎收看不等式教学

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这是不等式是代数里其中一种程序

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让我们就开始吧!

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一开始我们先来看一下

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说 X > 5 好了

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这是说 X 可以是 5.01, 可以是 5.5, 也可以是一百万

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可是 X 不能是 4 或是 3 或 0 或 -8

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不然這樣吧

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我们画一条数字线

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这样看比较方便一点

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如果这是 5, X 先是不能等于 5

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那我们就画一个圆圈在这边

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然后把 X 的可能数值都涂上颜色

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之前说过, X 可以是 5.000001

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因为 X 只需要比 5 大一点而已

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所以只多了 0.000001 也算可以

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那我们就在举几个例子吧

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6 也是比 5 大, 10 也是

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100 也是成立

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好, 现在如果把这算是程序

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程序或不等式的两边

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都乘以或除以 -1, 那会怎样呢?

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来想一想, -X 和 -5 中间有甚么关系?

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我说的关系是

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-X 是比 -5 大还小呢?

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记得我们说过 X 有可能是 6

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那 -6 的话, 是比 -5 大还小?

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-6 比 -5 小, 对吧?

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再回到数字在线

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看一下这 -5, 先把它圈起来

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因为这是不等式

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只有大于和小于

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所以一定不会是等于 5

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好, X 是有可能是 6

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所以我们画 -6 在这一边

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-6 比 -5 小

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当然 -10, -100, 负一百万也比 -5 小啦

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所以呢, -X 是比 -5 小

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你只需要记得这一点

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计算代数不等式

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基本上跟算一般方程式一样

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< 小于和 > 大于跟 = 等号都一样的计算

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唯一的分别是

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当你在乘除的时候

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要把 > 和 < 倒过来

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你只要记得这个就好了

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那我们来试一些例子吧

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要记得

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X > 5 就是 -X < -5

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甚么数字都一样

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记住这个就可以有一个直觉

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看到问题就知道怎么着手

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例如说 3X + 2 是 ≤ 1

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这挺简单的

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先看 3X 这一边, 两边都要减掉 2

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记得在加或者减的时候

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符号是不用换的

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所以在减掉 2 之后

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3X 就是 ≤ -1 了, 对吧?

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然后我们就从两边都除以 3

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所以 X 就是 ≤ -1/3

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你看我们其它甚么都没改

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因为刚刚是除以 +3

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还可以吧? 来试一下另一个算法

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我们先从两边都减去 1

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跟之前不一样

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现在就变成 3X + 1 是 ≤ 0

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刚刚是两边都减掉 1

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现在再从两边都减去 3X

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变成 1 ≤ -3X

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因为我从左边减了 3X

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就要从右边也减 3X

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现在就得从两边都除以一个负数了

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对吗? 两边都得除以 -3

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这一边是 -1/3

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就像刚刚学的

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因为现在是除以负数

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不等式的符号就得反过来了

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本来是小于或等于

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现在就是 ≥ X

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我们是否用两种不同的方法得到同样的答案？

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这两边都减去 5X, -13X + 7 > 2

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现在是 - 1/3 ≥ X

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同样的答案，对不？

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X 小于或等于 1/3

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这是我喜欢代数的原因

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你总可以有多种方法解决一个问题

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你得到正确的答案只要你做得对

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我们来做几个题目

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擦干净。。。下面做一个稍微有点难度的题目

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比如 - 8x + 7 > 5x +2

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从两边减去 5X

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- 13x + 7 > 2

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先从两边都减去 7

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变 -13X > -5

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然后再从两边都除以 -13

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这非常简单

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一边是 X, 另一边是 -5 除以 -13, 也就是 5/13

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因为俩负号互相取消掉了

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记得我们是除了一个负数

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所以不等式符号得反过来

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X < 5/13

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跟本来算的一样

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不相信我的话, 可以找些数字试试看

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记得我一开始学这个的时候

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我也不相信老师说的, 然后试代进了一些数字

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之后我就知道这真的是这样算的

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当你在两边除以或乘以

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一个负数的时候, 符号得反过来

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要切记, 只有在乘除的时候需要这样做

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加减的时候是不用的

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现在你应该

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大既有个慨念了吧?

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这其实没有甚么新的算法

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这不等式

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或者说不等方程式

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跟正常的线性方程式是一样的

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唯一不一样的是

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当你从两边乘以除以一个负数

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要记得把符号给倒过来

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现在你准备好做练习题了吗?

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加油!