这部分需要会什么？
- 解一元一次不等式并表示解集
- 识别端点是否包含与边界线是否实线
- 检验二元线性不等式的公共可行域
核心概念与公式
不等式两边加减同一个数，不等号方向不变；乘除正数方向不变，乘除负数必须反向。例如 \(-2x>6\) 等价于 \(x<-3\)。复合不等式的“且”表示交集，“或”表示并集。
二元不等式先画边界直线，再用不在边界上的测试点判断哪侧满足。\(\le\)、\(\ge\) 包含边界，使用实线；\(<\)、\(>\) 不含边界，使用虚线。可行域需同时满足全部条件。
做题时怎样使用
- 将文字中的至少、至多、超过分别转成对应不等号
- 解不等式；涉及负数乘除时特别检查方向
- 若变量表示人数、件数等，再在解集中选整数，并核对端点
容易混淆的地方
“至少 5”包括 5；“大于 5”不包括 5。图上的某点满足一个条件，并不代表它满足整个不等式组。
用一个例题串起方法
知识点教学例题一项活动收取固定费用 18 元，每位参加者另付 7 元。总预算不超过 60 元，最多可有多少位参加者？
展开解题思路 ＋
设人数为非负整数 \(n\)，则 \(18+7n\le60\)，所以 \(n\le6\)。最大人数为 6，此时费用恰好为 60 元。
本知识点题库
先独立作答，再查看答案与解析。
线性不等式与可行域进阶
An arborist studying forestland in Illinois estimates that there are at least 50 and no more than 60 hickory trees per acre in a certain forest. Which of the following best represents the arborist's estimate of the number of hickory trees, x, that are in a 3-acre section of this forest?
原库参考解析
线性不等式与可行域进阶
The shaded region shown represents the solutions to which inequality?
原库参考解析
线性不等式与可行域进阶
A freight elevator can hold a maximum weight of 5,450 pounds during one trip. A 190-pound person needs to deliver several boxes using the freight elevator. Some of these boxes weigh 23 pounds each and the others weigh 60 pounds each. Which inequality represents the possible combinations of the number of 23-pound boxes, x, and the number of 60-pound boxes, y, the person can deliver during one trip if only the person and the boxes are on the freight elevator?
原库参考解析
线性不等式与可行域挑战
\( y>2x−72 \)
\( y<−\frac{1}{6}x−9 \)
For which of the following tables are all the values of x and their corresponding values of y solutions to the given system of inequalities?
原库参考解析
线性不等式与可行域进阶
A freight elevator can hold a maximum weight of 4,840 pounds during one trip. A 170-pound person needs to deliver several boxes using the freight elevator. Some of these boxes weigh 21 pounds each and the others weigh 62 pounds each. Which inequality represents the possible combinations of the number of 21-pound boxes, x, and the number of 62-pound boxes, y , the person can deliver during one trip if only the person and the boxes are on the freight elevator?
原库参考解析
线性不等式与可行域挑战
\( y<x \)
\( y>−3x−11 \)
For which of the following tables are all the values of x and their corresponding values of y solutions to the given system of inequalities?
原库参考解析
线性不等式与可行域挑战
A giant panda is predicted to have a mass between \( \frac{1}{950} \)and \( \frac{1}{850} \) times its mother's mass when it is born. If its mother is predicted to have a mass of 95,950 grams when the giant panda is born, which inequality best represents the prediction of the giant panda's mass p, in grams, when it is born?
原库参考解析
线性不等式与可行域挑战
The shaded region shown represents the solutions to which inequality?
原库参考解析
线性不等式与可行域挑战
\( y<−3x+18 \)
Which point \( (x,\ y) \) is a solution to the given inequality in the xy-plane?
原库参考解析
线性不等式与可行域进阶
The shaded region shown represents the solutions to which inequality?
原库参考解析
线性不等式与可行域挑战
\( y>19 \)
\( 3x+y<26 \)
The point \( (x,\ 44) \) is a solution to the given system of inequalities in the xy-plane. Which of the following could be the value of \( x \)?
原库参考解析
线性不等式与可行域进阶
A pet service that takes care of both cats and dogs can care for at most 43 animals. Which inequality represents this situation, where c is the number of cats and d is the number of dogs?
原库参考解析
