已知
、
在数轴上分别表示
、
,
(1)对照数轴填写下表:
(2)若
、
两点间的距离记为
,试问
和
、
(
)的数量关系是________;
(3)写出数轴上到
和
的距离之和为
的所有整数,并求这些整数的和;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/9eb4e89f-8204-4daa-9650-7c340330df20.png?resizew=337)
(4)若点
表示的数为
,当
取最小值时,相应的
的取值范围是________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)对照数轴填写下表:
6 | 2 | ||||
4 | 0 | ||||
| 2 | 0 |
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
(3)写出数轴上到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a060c710d4fb153aa74cfd2418b6ffa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7f959148f8da15d2a4a4ceb30745df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/9eb4e89f-8204-4daa-9650-7c340330df20.png?resizew=337)
(4)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cfb936d8d761ccbe51b7892bd898a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
更新时间:2023-12-13 22:44:21
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相似题推荐
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【推荐1】如图,在数轴上点
分别表示
且点
在点
的左侧,点
在点
的右侧
![](https://img.xkw.com/dksih/QBM/2020/8/31/2539938160214016/2541206689193984/STEM/a793090fd88a4dfabb29b771a822cf36.png?resizew=349)
(1)求
的取值范围;
(2)当
时,
的值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed4f74702bc84caf492ee7eff4baefc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2020/8/31/2539938160214016/2541206689193984/STEM/a793090fd88a4dfabb29b771a822cf36.png?resizew=349)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4b0a454f28f2af03a55a8db88ce660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐2】阅读材料,回答问题:
如图1,点
在数轴上对应的数分别为
. 若点
在数轴上,且
,则点
表示的数为
. 理由如下:
设点
表示的数为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
,
,
.
.
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/0250e318-7f07-4877-bab6-d5154e1154ca.jpg?resizew=599)
(1)如图2,点
在
两点之间,对应的数分别为
,且
.
①若
,
,则
,
;
②小明同学认为:
,
,你同意吗?若同意,请证明;若不同意,请说明理由;
(2)如图3,点
在
两点之间,对应的数为
,且
. 则
(用含
的代数式表示).
如图1,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f89a8b5cf6996a6455375e405bfb9d.png)
设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e6ea4fd9578f3282c5a63e64a7a987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f883ed9aa7bdbad1cd4e7ac6ba48c03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7732af6dfede9687ca643be188ef383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e54920f4535faf002ad7ed04aea8c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/0250e318-7f07-4877-bab6-d5154e1154ca.jpg?resizew=599)
(1)如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa69fd8445d01c98634c2e885b47d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d708cb763716467219215cdc0782c0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471f7ddc061db5c6cd5cf3199325410a.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23725094c363fd158166a8698971694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
②小明同学认为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6060d6b4ca516bede564ee6782ca31cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df09d48b933ba10334cffe8dd84010f.png)
(2)如图3,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d989a6242d9e0eafff15859bf35b3feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d4c3c5be92530fde668fe0a43c1afe.png)
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【推荐3】数轴是一个非常重要的数学工具,它使数和数轴上的点建立起对应关系,揭示了数与点之间的内在联系,它是“数形结合”的基础.
例如:从“形”的角度看:
可以理解为数轴上表示3和1的两点之间的距离;
可以理解为数轴上表示3与
的两点之间的距离.
从“数”的角度看:数轴上表示4和
的两点之间的距离可用代数式表示为:
.
根据以上阅读材料探索下列问题:
(1)数轴上表示2和
的两点之间的距离是______;
______;
______;(直接写出最终结果)
(2)等式
几何意义______,则
的值为______;
(3)若
为数轴上某动点表示的数,则式子
有最小值吗?若有求出最小值,若没有,写出理由.
例如:从“形”的角度看:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2869da93f8f90e6f051d44d9f57ea2d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d16f85eb6153943993c61d136fe58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
从“数”的角度看:数轴上表示4和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89efc56c7293d4351c76ec02fff9a7e6.png)
根据以上阅读材料探索下列问题:
(1)数轴上表示2和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157f1c1567a7ca3ad399fe2e40bf16ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b68de8ef07fd9978c79e11fcba5b06.png)
(2)等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3036e0abea8bfbeb4f39e54678fdd6c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2805faa31b7022495ddbbaea613d04.png)
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【推荐1】如图是某一条东西方向直线上的公交线路的部分路段,西起A站,东至
站,途中共设12个上下车站点.某天,小明参加该路线上的志愿者服务活动,从
站出发,最后在某站结束服务活动.如果规定向东为正,向西为负,当天的乘车站数按先后顺序依次记录如下(单位:站):
,
,
,
,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/5/3b52a984-4861-4ac2-b2bc-481c4600446d.png?resizew=404)
(1)请通过计算说明结束服务的“某站”是哪一站?
(2)若相邻两站之间的平均距离约为2.5千米,求这次小明志愿服务期间乘坐公交车行进的总路程约是多少千米?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ceec0d3f3d8d2978fe4729c70fd991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63351a5a9bb27f78dd6fe097acc933d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6489852d310f01375f213b3bdf0406c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497f79b82f7428fd4ad48fb472b2ef13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497f79b82f7428fd4ad48fb472b2ef13.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/5/3b52a984-4861-4ac2-b2bc-481c4600446d.png?resizew=404)
(1)请通过计算说明结束服务的“某站”是哪一站?
(2)若相邻两站之间的平均距离约为2.5千米,求这次小明志愿服务期间乘坐公交车行进的总路程约是多少千米?
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【推荐2】已知有理数m和n互为相反数,a和b互为倒数,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f81f63dcb68a4a70a24ecb8602f589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cb791987c6c2562899929baac7ea7c6.png)
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【推荐1】材料阅读:已知点A、B在数轴上分别表示有理数a、b,|a﹣b|表示A、B两点之间的距离.
如:|1﹣2|表示数轴上1与2两点之间的距离,所以数轴上1与2两点之间的距离是|1﹣2|=1.
(1)数轴上表示﹣2和﹣5的两点之间的距离是 ;
(2)数轴上表示x和﹣1的两点A和B之间的距离是 ,如果|AB|=2,那么x为 ;
(3)若x表示一个有理数,则|x﹣1|+|x+3|有最小值吗?若有,请求出最小值;若没有,请说明理由.
如:|1﹣2|表示数轴上1与2两点之间的距离,所以数轴上1与2两点之间的距离是|1﹣2|=1.
(1)数轴上表示﹣2和﹣5的两点之间的距离是 ;
(2)数轴上表示x和﹣1的两点A和B之间的距离是 ,如果|AB|=2,那么x为 ;
(3)若x表示一个有理数,则|x﹣1|+|x+3|有最小值吗?若有,请求出最小值;若没有,请说明理由.
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【推荐2】有6筐白菜,以每筐25千克为标准质量,超过的千克数记作正数,不足的千克数记作负数,称量后的记录如图.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/8e549f14-9fb4-41fc-b2ae-2f564ae6c0ba.png?resizew=475)
请回答下列问题:
(1)这6筐白菜中最接近标准质量的这筐白菜为 ____________千克.
(2)与标准质量相比,这6筐白菜总计超过或不足多少千克?
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/8e549f14-9fb4-41fc-b2ae-2f564ae6c0ba.png?resizew=475)
请回答下列问题:
(1)这6筐白菜中最接近标准质量的这筐白菜为 ____________千克.
(2)与标准质量相比,这6筐白菜总计超过或不足多少千克?
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