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基础
\( y>-36 \)
Which shaded region represents the solutions to the given inequality?
原库参考解析
线性不等式与可行域基础
Carmen needs at least 100 signatures to submit a petition. If Carmen already has 51 signatures, what is the minimum number of additional signatures Carmen needs to submit the petition?
原库参考解析
线性不等式与可行域进阶
In the xy-plane, which of the following does NOT contain any points that are part of the solution set to \( 5x−7y>35 \)?
原库参考解析
线性不等式与可行域挑战
Zuri has a goal to run at least 16 miles per week while training for a race. This week, she has run 4 miles. If x represents the additional number of miles Zuri needs to run this week to meet her goal, which inequality represents this situation?
原库参考解析
线性不等式与可行域进阶
In the xy-plane, which of the following does NOT contain any points that are part of the solution set to \( 7x−6y>42 \)?
原库参考解析
线性不等式与可行域进阶
An event planner is planning an ice-skating event. It costs the event planner a onetime fee of $35 to rent the skating rink and $15.25 per attendee. The event planner has a budget of $225. What is the greatest number of attendees possible without exceeding the budget?
原库参考解析
线性不等式与可行域进阶
On a certain day in June, the lowest recorded wind speed in a town was 5 miles per hour (mph) and the highest recorded wind speed was 14 mph. Which inequality is true for all values of w, where w represents any wind speed, in mph, recorded in the town on this day?
原库参考解析
线性不等式与可行域挑战
\( y<15x+13 \)
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
原库参考解析
线性不等式与可行域进阶
\( y<14x+12 \)
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
原库参考解析
线性不等式与可行域进阶
On a certain day in June, the lowest recorded wind speed in a town was 9 miles per hour (mph) and the highest recorded wind speed was 20 mph. Which inequality is true for all values of w, where w represents any wind speed, in mph, recorded in the town on this day?
原库参考解析
线性不等式与可行域进阶
For a party, 51 hamburger buns are needed. Hamburger buns are sold in packages of 12. What is the minimum number of packages that should be bought for the party?
原库参考解析
线性不等式与可行域挑战
\( y\ge33 \)
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
原库参考解析
