名校
1 . 阅读理解:
例1.解方程|x|=2,因为在数轴上到原点的距离为2的点对应的数为±2,所以方程|x|=2的解为x=±2.
例2.解不等式|x﹣1|>2,在数轴上找出|x﹣1|=2的解(如图),因为在数轴上到1对应的点的距离等于2的点对应的数为﹣1或3,所以方程|x﹣1|=2的解为x=﹣1或x=3,因此不等式|x﹣1|>2的解集为x<﹣1或x>3.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/6323e167-c8c1-46e4-81aa-990c0da70ca7.png?resizew=231)
参考阅读材料,解答下列问题:
(1)方程|x﹣2|=3的解为 ;
(2)解不等式:|x﹣2|≤1.
(3)解不等式:|x﹣4|+|x+2|>8.
(4)对于任意数x,若不等式|x+2|+|x﹣4|>a恒成立,求a的取值范围.
例1.解方程|x|=2,因为在数轴上到原点的距离为2的点对应的数为±2,所以方程|x|=2的解为x=±2.
例2.解不等式|x﹣1|>2,在数轴上找出|x﹣1|=2的解(如图),因为在数轴上到1对应的点的距离等于2的点对应的数为﹣1或3,所以方程|x﹣1|=2的解为x=﹣1或x=3,因此不等式|x﹣1|>2的解集为x<﹣1或x>3.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/6323e167-c8c1-46e4-81aa-990c0da70ca7.png?resizew=231)
参考阅读材料,解答下列问题:
(1)方程|x﹣2|=3的解为 ;
(2)解不等式:|x﹣2|≤1.
(3)解不等式:|x﹣4|+|x+2|>8.
(4)对于任意数x,若不等式|x+2|+|x﹣4|>a恒成立,求a的取值范围.
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2021-08-07更新
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1348次组卷
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3卷引用:四川省乐山市市中区2020-2021学年七年级下学期期末数学试题
四川省乐山市市中区2020-2021学年七年级下学期期末数学试题湖南省邵阳市第六中学2021-2022学年八年级上学期第二次月考数学试题(已下线)第一次月考难点特训(二)和绝对值的几何意义有关的压轴题-【微专题】2022-2023学年七年级数学上册常考点微专题提分精练(人教版)
2 . (1)解方程组:
;
(2)计算:
;
(3)解方程:
;
(4)解不等式组
,请按下列步骤完成解答.
(I)解不等式①,得__________________;
(Ⅱ)解不等式②,得_________________;
(Ⅲ)把不等式①和②的解集在数轴上表示出来:
原不等式组的解集为:__________________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05fb63da591653edf3abe88a8e0c140e.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae7b0a78aace550e04f9a65d6887ca0.png)
(3)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc8cd37e76438b63b15a2e3d80c11f6.png)
(4)解不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5683b7974117fff8aa416c389b985ff3.png)
(I)解不等式①,得__________________;
(Ⅱ)解不等式②,得_________________;
(Ⅲ)把不等式①和②的解集在数轴上表示出来:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
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3 . 阅读下列材料:
我们知道
的几何意义是在数轴上数x对应的点与原点的距离,即
,也就是说,
表示在数轴上数x与数0对应的点之间的距离;这个结论可以推广为
表示在数轴上数
与数
对应的点之间的距离;
例1.解方程
.因为在数轴上到原点的距离为2的点对应的数为
,所以方程
的解为
.
例2.解不等式
.在数轴上找出
的解(如图),因为在数轴上到1对应的点的距离等于2的点对应的数为
或3,所以方程
的解为
或
,因此不等式
的解集为
或
.
.由绝对值的几何意义知,该方程就是求在数轴上到1和
对应的点的距离之和等于5的点对应的x的值.因为在数轴上1和
对应的点的距离为3(如图),满足方程的x对应的点在1的右边或
的左边.若x对应的点在1的右边,可得
;若x对应的点在
的左边,可得
,因此方程
的解是
或
.
(1)方程
的解为________________;
(2)解不等式:
;
(3)解不等式:
.
我们知道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe916d05211cf74a2b1428a8bb8bbbbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c602171f16d22b78c9eb37a3b46b907a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe916d05211cf74a2b1428a8bb8bbbbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24acaad3e4a83c102702155e5df281e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
例1.解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494b364e4cd6665b8ab8d4d107f1885e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b8bee40319fe80e512d221cfe252a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494b364e4cd6665b8ab8d4d107f1885e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e88a7f9f2d8040d8451f06292200966.png)
例2.解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14ad13232a41d10e5fd9c8b1f6b44ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794cc67745c3003486c38e68b3317993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794cc67745c3003486c38e68b3317993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14ad13232a41d10e5fd9c8b1f6b44ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da6d82d173ad18cc040e94c925b5ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752455799e49f846e2601304fec5d3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c598972fe169aa5f71d6ae2e63f8b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c598972fe169aa5f71d6ae2e63f8b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
(1)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a79a71255807bdb301c526b997c921e.png)
(2)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823bd29b2af60ee939fe778fdffdeff2.png)
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/156dc6d364a9c6a6441f5e33fc284c7a.png)
您最近一年使用:0次
2024-05-07更新
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248次组卷
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2卷引用:福建省晋江市安海镇五校2023-2024学年七年级下学期期中联考数学试题
4 . 莉莉在归纳有理数运算时得到下列结论:对于任意两个有理数a,b,①如果
,那么
或者
.②如果
,那么
或者
,③如果
,那么
或者
,我们发现这些结论在整式运算中仍然成立.
例如,解不等式
.由不等式
可得:不等式组①
或不等式组②
,解不等式组①得:
,解不等式组②得
,∴不等式
的解集为
或
.请你完成下列任务.
(1)解方程:
;
(2)求不等式
的解集;
(3)求不等式
的解集﹔
(4)如果(1)中方程的两个解,都是关于x的不等式组
的解,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3019b662e5dc2750bb6f9199d3250f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17aa651392e64c5c95f14f59a0ec185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24483caba4aa37def32fe3c4e1ab1842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5fb45fa98fa3f0d6efd85d100d1c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c4db4f8e5f00a53b246f71e1f1578d.png)
例如,解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228c0b65b69e32dd0da60d90d4807151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228c0b65b69e32dd0da60d90d4807151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bbd13a2c8cd502f8ff61de2fb4f428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7925794131854c919d8fc22eb1c46a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c21c6260bcade05f3a432841f449b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228c0b65b69e32dd0da60d90d4807151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c21c6260bcade05f3a432841f449b5c.png)
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7654181e94f9689bbb3ef1cbf8cb592.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423db210c4ff9ac1c9b7d3b48b9727c5.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502bc2522f8378afccdfb4561e3155f9.png)
(4)如果(1)中方程的两个解,都是关于x的不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9514d1bc45b79b501b98ccff942fb50.png)
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5 . 解答下列各题.
(1)先化简,再求值:
÷
,其中x=
+1.
(2)分解因式:8(x2-2y2)-x(7x+y)+xy.
(3)解不等式
≤
-1,并把解集表示在数轴上.
![](https://img.xkw.com/dksih/QBM/2017/11/18/1819969393573888/1822923743346688/STEM/3651b39c0ad245c3976a6a7a7cdeaafb.png?resizew=182)
(4)解不等式组
并将解集在数轴上表示出来.
![](https://img.xkw.com/dksih/QBM/2017/11/18/1819969393573888/1822923743346688/STEM/18fde2ea31644d1ab3fd32f419c679c9.png?resizew=173)
(5)解方程:
+
=4.
(1)先化简,再求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac093363e511954b6da185d1a7cbec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87c556bdb25cfdc56deb388994136d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
(2)分解因式:8(x2-2y2)-x(7x+y)+xy.
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624e71c47dcf0230ebca3d95f58d6bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1c9ae28e79df58732e331765f24506.png)
![](https://img.xkw.com/dksih/QBM/2017/11/18/1819969393573888/1822923743346688/STEM/3651b39c0ad245c3976a6a7a7cdeaafb.png?resizew=182)
(4)解不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addffbdd642de16d9d0a2ef216997720.png)
![](https://img.xkw.com/dksih/QBM/2017/11/18/1819969393573888/1822923743346688/STEM/18fde2ea31644d1ab3fd32f419c679c9.png?resizew=173)
(5)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d682696876e168f7f5dc0dc68965ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fefe195bba3da998abf698060fcd89b5.png)
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名校
6 . 阅读理解:
表示5与
之差的绝对值,实际上也可理解为5与
两数在数轴上所对的两点之间的距离.
例1. 解方程
,因为在数轴上到原点的距离为2的点对应的数为
,所以方程
的解为
;
例2. 解不等式
,在数轴上找出
的解(如图),因为在数轴上到1对应的点的距离等于2的点对应的数为
或3,所以方程
的解为
或
,因此不等式
的解集为
或
.
(1)
的解为____________;
(2)找出所有符合条件的整数
,使得
,这样的整数是____________;
(3)不等式
的解集为____________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7ba690de4bdbdceb968265181a208f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
例1. 解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e23117608becdb000a9812d7fe9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b8bee40319fe80e512d221cfe252a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e23117608becdb000a9812d7fe9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e88a7f9f2d8040d8451f06292200966.png)
例2. 解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f7c6d752d770babee942434e1e5e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015bb51577c2c3c63d40e5b3f0ed5b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015bb51577c2c3c63d40e5b3f0ed5b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1c84057882768f20a01365c81b6760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f7c6d752d770babee942434e1e5e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da6d82d173ad18cc040e94c925b5ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752455799e49f846e2601304fec5d3b8.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bd2967c563c4627572be3b9482cfe1.png)
(2)找出所有符合条件的整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e7f5f0b2e6fb447b5050a3c3fda074.png)
(3)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052895c4466ee13b79b210720fb4141d.png)
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2023-07-26更新
|
398次组卷
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4卷引用:上海市进才实验中学2022-2023学年六年级下学期期中数学试题
上海市进才实验中学2022-2023学年六年级下学期期中数学试题(已下线)第二章第02讲 一元一次不等式及与一次函数(9类热点题型讲练)-【帮课堂】2023-2024学年八年级数学下册同步学与练(北师大版)(已下线)专题01 有理数(6大考点经典基础练+优选提升练)-【好题汇编】备战2023-2024学年六年级数学下学期期中真题分类汇编(沪教版)(已下线)上海市六年级下学期期中模拟03(沪教版:有理数、一次方程(组)和一次不等式) -2023-2024学年六年级数学下学期期中考点大串讲(沪教版)
7 . 阅读理解:
例1.解方程
,因为在数轴上到原点的距离为2的点对应的数为
,所以方程
的解为
.
例2.解不等式
,在数轴上找出
的解(如图),因为在数轴上到1对应的点的距离等于2的点对应的数为
或3,所以方程
的解为
或
,因此不等式
的解集为
或
.
参考阅读材料,解答下列问题:
(1)方程
的解为________
(2)解不等式:
.
(3)解不等式:
.
例1.解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e23117608becdb000a9812d7fe9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b8bee40319fe80e512d221cfe252a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e23117608becdb000a9812d7fe9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e88a7f9f2d8040d8451f06292200966.png)
例2.解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f7c6d752d770babee942434e1e5e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015bb51577c2c3c63d40e5b3f0ed5b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015bb51577c2c3c63d40e5b3f0ed5b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f7c6d752d770babee942434e1e5e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da6d82d173ad18cc040e94c925b5ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752455799e49f846e2601304fec5d3b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/20/039ae46b-2b5e-49ec-b77e-65c7f196c0fb.png?resizew=350)
参考阅读材料,解答下列问题:
(1)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342e44ab6b4cb9a16afa2804fad04d21.png)
(2)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f223b8402b00138ff51ca20db54bb87.png)
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e75f67b762010dead0757ac9dfa0f32.png)
您最近一年使用:0次
2023-09-15更新
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586次组卷
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6卷引用:福建省厦门市杏南中学2022-2023学年七年级下学期月考数学试题
福建省厦门市杏南中学2022-2023学年七年级下学期月考数学试题(已下线)专题3.2 一元一次不等式【九大题型】-2023-2024学年八年级数学上册举一反三系列(浙教版)(已下线)第08讲 一元一次不等式-【寒假自学课】2024年八年级数学寒假提升学与练(北师大版)(已下线)专题02 方程与不等式(5大易错点分析+19个易错点+易错题通关)-备战2024年中考数学考试易错题(江苏专用)山东省济南天桥区泺口实验中学2023-2024学年八年级下学期3月第一次月考数学试题(已下线)清单05 一元一次不等式 全章复习(4个考点梳理+10种题型+3类型)-2023-2024学年七年级数学下学期期末考点大串讲(苏科版)
8 . 解方程或计算
(1)解方程组
;
(2)
;
(3)先化简,再求值(x﹣1)(x﹣2)﹣(x+1)2,其中x=
;
(4)已知x2﹣4x﹣1=0,求代数式(2x﹣3)2﹣(x+y)(x﹣y)﹣y2的值.
(1)解方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32dc8b94f80dcad34d7a981d03e1bd04.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8198909b46d6aa42d0bf31fe4a68868.png)
(3)先化简,再求值(x﹣1)(x﹣2)﹣(x+1)2,其中x=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(4)已知x2﹣4x﹣1=0,求代数式(2x﹣3)2﹣(x+y)(x﹣y)﹣y2的值.
您最近一年使用:0次
9 . (1)计算:
;
(2)先化简再求值:
,其中
;
(3)解不等式组
,并把解集在数轴上表示出来.
(4)解方程:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b36c552b6188d475d20d46e97b2d14.png)
(2)先化简再求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4565d2cba3d60fb4adf80eba293692c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fcd8dd9c04eeb4ecd386b47d528d948.png)
(3)解不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c120ad64b48a3fe9777090d3c103c5.png)
(4)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ea38f7d031fbf276f243d657e0c813.png)
您最近一年使用:0次
10 . 阅读下列材料:我们知道
表示的是在数轴上数
对应的点与原点的距离,即
,也就是说,
表示在数轴上数
与数
对应点之间的距离
这个结论可以推广为
表示在数轴上数
,
对应点之间的距离.
例如:解方程
.
解:
,
在数轴上与原点距离为
的点对应的数为
,即该方程的解为
.
【理解应用】根据绝对值的几何意义可以解一些绝对值不等式.
我们定义:形如“
,
,
,
”
为非负数)的不等式叫做绝对值不等式,能使一个绝对值不等式成立的所有未知数的值称为绝对值不等式的解集.
由图
可以得出:绝对值不等式
的解集是
或
,
绝对值不等式
的解集是
.
例如:解不等式
.
解:如图
,首先在数轴上找出
的解,即到
的距离为
的点对应的数为
,
,则
的解集为到
的距离大于
的点对应的所有数,所以原不等式的解集为
或
.
参考阅读材料,解答下列问题:
(1)方程
的解为______ .
(2)不等式
的解集是______ .
(3)不等式
的解集是______ .
(4)不等式
的解集是______ .
(5)若
对任意的
都成立,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc51e97939a8966daa015535a801561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeec4df122bbd73153ca41d6e4e9263c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc51e97939a8966daa015535a801561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
例如:解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fcafe862fb78982464e73f4c4d77ca.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4c17e05ff5eb2e0a5bd623719efc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39fa8414146b94d4b04cd4ca6f4ef93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d8f29c8067780dcf8553355f36b3e7.png)
【理解应用】根据绝对值的几何意义可以解一些绝对值不等式.
我们定义:形如“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaac03be2bdc3eb32fa5cfd0d4e2106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb58390186f37dcf6e53698d9cc712d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24fbeccfbdec8ec998e614de522bcda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11978d4a5f24f29407c78f1f2d47dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618fa538346aadfd9dd265aacb525203.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/21/32edf1ea-9622-4205-8f40-61b694ffeb4a.png?resizew=553)
由图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e38581b43f437454b86dae0daed9a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da6d82d173ad18cc040e94c925b5ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
绝对值不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bea5d2fd180d2272b6d28f61ead429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18aca0e7da68266cda4d4af074a3d02.png)
例如:解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f7c6d752d770babee942434e1e5e72.png)
解:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015bb51577c2c3c63d40e5b3f0ed5b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f7c6d752d770babee942434e1e5e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da6d82d173ad18cc040e94c925b5ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752455799e49f846e2601304fec5d3b8.png)
参考阅读材料,解答下列问题:
(1)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a846bf9735ef245ededb7108bcaae54a.png)
(2)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73321368e9b0043300c5f468b6619d23.png)
(3)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eca8a6bedc0a46ddd7b60f2a0348e3d.png)
(4)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d450c191e906f396159130bf8d6810.png)
(5)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d3ee273391177b5ea4ee6dad4e129b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-07-16更新
|
170次组卷
|
2卷引用:江苏省扬州市梅岭教育集团2022-2023学年七年级下学期第二次段考数学试题