名校
1 . 小明在解方程
去分母时,方程右边的
漏乘了12,因而求得方程的解为
,求
的值及原方程的解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57a6c043aa1d97c5bbfcb25fc1ded33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-03更新
|
110次组卷
|
17卷引用:四川省德阳市第五中学2017-2018学年七年级半期考试数学试卷
四川省德阳市第五中学2017-2018学年七年级半期考试数学试卷江西省宜春市袁州区宜阳学校2020-2021学年七年级上学期第二次月考数学试题(已下线)练习10 解一元一次方程专练-2020-2021学年【补习教材·寒假作业】七年级数学(湘教版)山东省德州市宁津县育新中学2020-2021学年七年级上学期第二次月考数学试题山东省济宁市金乡县2020-2021学年七年级上学期期末数学试题江苏省无锡市江阴市青阳片2020-2021学年七年级上学期12月月考数学试题福建省泉州市晋江市海片区2020-2021学年七年级下学期期中数学试题湖南省长沙市开福区青竹湖湘一外国语学校2021-2022学年七年级上学期第三次月考数学试题河北省张家口市等2地三河市燕灵路中学等2校2022-2023学年七年级上学期月考数学试题广东省韶关市武江区广东韶关实验中学 2021-2022学年七年级上学期期中数学试题山东省日照市东港区新营中学2023-2024学年七年级上学期12月月考数学试题山东省齐河县安头乡中学2023-2024学年上学期七年级复习模拟考试数学试题河南省安阳市内黄县第五实验学校2023-2024学年七年级上学期第三次月考考试数学试题陕西省西安市西咸新区沣西新城第二学校2023-2024学年七年级学期月考数学试题山东省德州市禹城市张庄镇中学2023-2024学年七年级上学期第二次月考数学试题河南省周口市郸城县2023-2024学年七年级下学期4月月考数学试题福建省泉州市培元中学2023-2024学年七年级下学期第一次月考数学试题
2 . 一同学在解方程
时,因看错了
的符号而得方程的解为
,试求
的值并正确地解方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb8c0267d7c47d0d00e404b9e9f5a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
3 . 定义一种新运算“▲”,其运算方式如下:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7121623625ecc34322ce5f76a98c18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72abd9ab67fb8e8032c06bb85e05bae7.png)
……
观察式子的运算方式,请解决下列问题:
(1)这种运算方式是:
________(用含m,n的式子表示);
(2)解方程:
;
(3)若关于x的方程:
的解为整数,求正整数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7121623625ecc34322ce5f76a98c18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72abd9ab67fb8e8032c06bb85e05bae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d74cbed7c4b571c6cb207905190e9a11.png)
观察式子的运算方式,请解决下列问题:
(1)这种运算方式是:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd1f465662e4de9508a6d33f1d34abd.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b6af41536129180b0544257add56a6.png)
(3)若关于x的方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50e80d2a1b78d005be23f73e9c7bd22.png)
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2023七年级上·浙江·专题练习
4 . 根据绝对值定义,若有
,则
或
,若
,则
,我们可以根据这样的结论,解一些简单的绝对值方程,例如:
解:方程
可化为:
或
,
当
时,则有:
,所以
,
当
时,则有:
;所以
,
故,方程
的解为
或
.
(1)解方程:
;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ccd888d9ccae6931263cc5aaaba937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5083e03a28e5ae0b5370ba1d09e5fca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbddb9f3f3f751b67388a739eed64cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e0e2f3a4ed81af3ec5d1359e58e3bc.png)
解:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e0e2f3a4ed81af3ec5d1359e58e3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f31f5724b4aa582fd656beff4372144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9412a9f0de450840020455380a6b5.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f31f5724b4aa582fd656beff4372144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dd4309a62b19cbf323384f8e91358f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9412a9f0de450840020455380a6b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d035a692e9eab83754e63c433c55b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
故,方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e0e2f3a4ed81af3ec5d1359e58e3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f1891a1b455b1460d761a9fa429426.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0b172c4b9845b2124fa7c6fb492348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
5 . 根据绝对值定义,若有
,则
或
,若
,则
,我们可以根据这样的结论,解一些简单的绝对值方程,例如:
.
解:方程
可化为:
或
,
当
时,则有:
,所以
,
当
时,则有:
;所以
,
故,方程
的解为
或
,
(1)解方程:
;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ccd888d9ccae6931263cc5aaaba937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395addb4439331615a7f220289d8b62c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5083e03a28e5ae0b5370ba1d09e5fca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbddb9f3f3f751b67388a739eed64cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e0e2f3a4ed81af3ec5d1359e58e3bc.png)
解:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e0e2f3a4ed81af3ec5d1359e58e3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f31f5724b4aa582fd656beff4372144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9412a9f0de450840020455380a6b5.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f31f5724b4aa582fd656beff4372144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dd4309a62b19cbf323384f8e91358f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9412a9f0de450840020455380a6b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d035a692e9eab83754e63c433c55b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
故,方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e0e2f3a4ed81af3ec5d1359e58e3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f1891a1b455b1460d761a9fa429426.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0b172c4b9845b2124fa7c6fb492348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b33ceacb7836ccd98815e08a20cd2be.png)
您最近一年使用:0次
2023-12-15更新
|
87次组卷
|
8卷引用:苏科版七年级上册数学期中测试卷(3)
苏科版七年级上册数学期中测试卷(3)(已下线)专题3.4 解一元一次方程(一)——合并同类项与移项(知识讲解)-2022-2023学年七年级数学上册基础知识专项讲练(人教版)吉林省白城市洮北区第三中学2022-2023学年七年级上学期期中数学试题(已下线)专题5.4 求解一元一次方程(一)-合并同类项与移项(知识讲解)-2022-2023学年七年级数学上册基础知识专项讲练(北师大版)辽宁省大连市金普新区2023-2024学年七年级上学期期中数学试题江苏省扬州市江都区江都区第二中学2023-2024学年七年级上学期期中数学试题(已下线)清单08 解一元一次方程(1个考点梳理+12种题型解读+提升训练)-2023-2024学年七年级数学上学期期末考点大串讲(苏科版)福建省泉州市永春县崇贤中学2023-2024学年七年级下学期月考数学试题
6 . 先化简,再求值:
(1)
,其中
,
.
(2)如图,是计算流程图,若输出的结果是4,求输入的数x.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65adae10078d1ac53515fcfc829d034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0c91693328b9a49178615dac21fae0.png)
(2)如图,是计算流程图,若输出的结果是4,求输入的数x.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/11/9b043408-859f-44f7-9eae-d596d679a5bf.png?resizew=437)
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2022-09-09更新
|
144次组卷
|
2卷引用:河南省周口市川汇区2021-2022学年七年级上学期期末数学试题
7 . 在解含有字母系数的方程时,常常将字母系数看作已知数,然后利用解方程的步骤和方法求解,所得的未知数的值常常是含有字母的代数式.
例如:解关于x的一元一次方程
其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aed0bfba78e2be6a0a8c500ce0eb8a1.png)
解:移项:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230692b0799f6b620ab93a61cc1ecace.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/3d3cb17e-8b4e-437e-8db3-ec2facc72e26.png?resizew=355)
合并同类项:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac7cb01686f5ac5b07eb5bb12d10027.png)
![](https://img.xkw.com/dksih/QBM/2023/11/8/3363397907439616/3365226642366464/STEM/fa48af97cd704ef7a9b5c1be51b62148.png?resizew=359)
因为
,所以
,
![](https://img.xkw.com/dksih/QBM/2023/11/8/3363397907439616/3365226642366464/STEM/864c4d9ac0584d1e8a68eee0fba575b6.png?resizew=359)
化系数为1,两边同除以
,得:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a531fb3e004edd6b26167be6bf60e34d.png)
(1)请仿照上面的方法解关于x的方程:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926d345839fc7d5f13f448b5c7d3e375.png)
(2)关于x的方程
,其中
,方程的解为正整数,求符合条件的k的整数值.
例如:解关于x的一元一次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1705f3d359c092102aabb761dfa934a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aed0bfba78e2be6a0a8c500ce0eb8a1.png)
解:移项:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230692b0799f6b620ab93a61cc1ecace.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/3d3cb17e-8b4e-437e-8db3-ec2facc72e26.png?resizew=355)
合并同类项:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac7cb01686f5ac5b07eb5bb12d10027.png)
![](https://img.xkw.com/dksih/QBM/2023/11/8/3363397907439616/3365226642366464/STEM/fa48af97cd704ef7a9b5c1be51b62148.png?resizew=359)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aed0bfba78e2be6a0a8c500ce0eb8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f11d2ae47825175beccadb36ed95e.png)
![](https://img.xkw.com/dksih/QBM/2023/11/8/3363397907439616/3365226642366464/STEM/864c4d9ac0584d1e8a68eee0fba575b6.png?resizew=359)
化系数为1,两边同除以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d311d7fed77ef4bd8e077d8e8f6aa4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a531fb3e004edd6b26167be6bf60e34d.png)
(1)请仿照上面的方法解关于x的方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926d345839fc7d5f13f448b5c7d3e375.png)
(2)关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f9e9936544d876f164e74f14e07873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5371fa518863c0d328d90b1e8d1c2deb.png)
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8 . “没有欧拉的众多科学发现,我们将过着完全不同的生活.”18世纪伟大的数学家欧拉,他创造并推广了大量数学符号,使数学更容易表述.他最先把关于x的多项式用符号
的形式来表示,把x等于a时的多项式的值用
.来表示,例如,当
时,
的值可以记为
即
.
(1)已知,
,
①
___________;②若
,则x的值为___________
(2)已知
,若
,
,求
的值.
(3)我们把方程
的解称为多项式
的“华益值”,试探索多项式
是否存在“华益值”?若存在,请求出“华益值”;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e39f6bbfd21f57e92d0b6797067e5cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e971d85d2eff43231cff24206609bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d561e45bd1956ea833f5917b555889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447792aa582e371e2dda14e21ac17afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecf2c232a261668e50a737992567ba8.png)
(1)已知,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ca3ef070783917ba04f969d0c74faa.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b834bc5004788fc38f6c4caa95e60c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204631611e8055443f7a4a9eebed6e7b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d627e3f93c42b88aaa24ffc1216984c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1887f80912fb444a51bdbcd6500d44b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dee7626efed368ecf40970a2ba5e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea1da12e9657e81b15bc8774fce72ec.png)
(3)我们把方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f563b3277f2fc80e46baf9aa7070d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e1e64e5336de6528d861850ec353ef.png)
您最近一年使用:0次
9 . 小军在解方程
去分母时,方程右边的
没有乘6,求得方程的解为
,求原方程的解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25478556664ba4ef4004459c741c8916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29418e5014731850c55565b6bf47aa41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
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10 . 嘉淇在解一元一次方程
□
时,发现常数“□”印刷不清楚.
(1)嘉淇假定常数“□”为2,解方程
□
.
(2)若这个方程的解为
,求常数“□”的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebbdc3d25b911fbd08b441878bf8c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e8813096732f5ca2b3f6d0f55d7d05.png)
(1)嘉淇假定常数“□”为2,解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebbdc3d25b911fbd08b441878bf8c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e8813096732f5ca2b3f6d0f55d7d05.png)
(2)若这个方程的解为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
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