不等式及其解集

-4 -3 -2 -1 0 1 2 3
归纳
观察数轴上所表示的下列两个解集，有 什么区别与联系？
(1) x 2
-4 -3 -2 -1 0 1 2 3 (2) x 2
-4 -3 -2 -1 0 1 2 Nhomakorabea3归纳
观察数轴上所表示的下列两个解集，有 什么区别与联系？ (5) x 1
3
-4 -3 -2 -1 0 1 2 3
小结
1、你学会了什么知识？ 不等式的定义 一元一次不等式的定义
不等式 不等式的解的定义
不等式的解集的定义
2、你有什么体会？ 不等式的解与解集的关系
用数轴表示不等式的解集的方法
作业
课本
P134
1、2、3
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范例
例2、直接写出下列不等式的解集，并 在数轴上表示出来：
(1) x 3 1
(2) 2x 4
(3) x 3 1
(4) 2x 4
(5) 3x 1
归纳
观察数轴上所表示的下列两个解集，有 什么区别与联系？
(1) x 2
-4 -3 -2 -1 0 1 2 3 (2) x 2
x 1.5 x 2 x 3 x 4
这个不等式有多少个解？ 你能找到使不等式不成立的值吗？
归纳
x23
使不等式成立的未知数x的值有：
x 1.5 x 2 x 3 x 4
不等式的解的定义：使不等式成立的未 知数的值叫不等式的解。
想一想：方程 x 2 3 的解是什么？
范例
例1、判断下列数中哪些是不等式 x 2 3 的解：
-3、-2.6、0、2、3、5、6、7.2
你还能找到不等式的解吗？
通过观察，你对不等式的解有什么发现？
探究
x23 你能在数轴上指出不等式的所有解吗？
-1 0 1 2 3 4 5 6 7
未知数的取值范围是：x 5
不等式的解集的定义：使不等式成立的 未知数的取值范围叫不等式的解集。
不等式及其解集
引入
观察下列式子：
2 1 2a 3b
2 1 3a 2b
a2 a2
不等式的定义：用“>、<、≤、≥、 ≠”表示不等关系的式子叫不等式。
新授
用不等式表示： (1)x的2倍大于1； (2)-2小于a的相反数； (3)a的2倍不大于3与a的和； (4) 3与b的差不小于b的3倍； (5)a与2的和不等于a与2的差； (6)a是正数； (7)a是非负数。
新授
观察下列式子：
2x 1
2 a
2a 3 a
3 b 3b
a2 a2
一元一次不等式的定义：含有一个未 知数，并且未知数的次数是1的不等式 叫一元一次不等式。
探究
不等式 x 2 3 中，使它成立的未知数 x的值有那些？请举出一些例子。
x23 使不等式成立的未知数x的值有：
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