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【329885】8.4 一元一次不等式组

时间:2025-02-07 09:22:28 作者: 字数:3554字


8.4 一元一次不等式组

一、选择题

1.若不等式组 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 有解,那么m的取值范围是(

A <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> B <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> C <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> D <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

2.满足不等式组 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的整数m的值有(

A1 B2 C3 D4

3.不等式组 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的最小整数解为(

A.-1 B0 C1 D4

二、填空题

1)用不等式表示x5倍与1的差不小于x的一半,应为_________

2)当 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 时,代数式 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的值小于-3

3)当 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 时,方程 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的解不小于-2

4)若 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> ,则 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的解集为________

5)不等式 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的负整数解为________

6)若不等式组 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的解集为 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> ,则 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

三、解答题

1.某校高一新生中有若干住宿生,分住若干间宿舍.若每间住4人,则还有21人无房住;若每间住7人,则有一间不空也不满.求住宿生人数.







2.把一篮苹果分给几个学生,若每人分4个,则剩下3个;若每人分6个,则最后一个学生所得到苹果不超过2个.求学生人数和苹果数.









3.某工人制造机器零件,如果每天比预计多做1件,那么8天所做零件数超过100件;如果每天比预计少做1件,那么8天所做零件数不到90件.这个工人预计每天做多少零件?





4.将若干只鸡放入若干个笼,若每个笼里放4只,则有1只鸡无笼可放;若每个笼里放5只,则有1笼无鸡可放,那么至少有几只鸡、几个笼?






5.每期《数学学习》发下来后,小俐同学都认真阅读,如果每天读5页,那么9天读不完,且第10天剩不足5页;如果每天读23页,那么2天读不完,且第3天剩不足23页.《数学学习》杂志每期有多少页?





6.先阅读下列例题的解答过程,然后完成后面的练习题.

例题:如果一个整式不等式只含有一个未知数,且未知数的最高次数是2,这种不等式叫一元二次不等式.例如 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 就是一元二次不等式.怎样解一元二次不等式 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 呢?先把 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 分解因式: <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

所以原不等式可化为 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 相乘得正,说明这两个因式同号,故原不等式可化为两个一元一次不等式组:

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

解不等式组Ⅰ得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> ,解不等式组Ⅱ得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

所以不等式 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的解集为 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

所以一元二次不等式 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的解集为 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

1)想一想:如果两个代数式相除得负数,这两个代数式的正负有什么规律?

2)求分式不等式 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 的解集(请试着写出解题过程).

参考答案

一、选择题

1C 2C 3B

二、填空题

1 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 2 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 3 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 4 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

5)-5,-4,-3,-2,-1 6 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

三、解答题

1.住宿生人数为5357

提示:设该校有宿舍x间,那么住校生有 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 名.根据题意,得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

解得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> .所以 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

2.有学生4人,苹果19个.

提示:设学生有x人,则苹果有 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 个.根据题意,得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

解得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

因为x是正整数,所以 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

3.这个工人预计每天做12件.

提示:设这个工人预计每天做x件,根据题意,得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

解得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

因为x是正整数,所以 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

4.至少有6个笼、25只鸡.

提示:设有x个笼,则有 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> 只鸡,根据题意,得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

解得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

5.该杂志每期有48页.

提示:设该杂志每期有x页,根据题意,得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

解得 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

因为页数是偶数,所以 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>

6. 1)这两个代数式应为一正一负 2)解集是 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a>