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
Ty set a goal to walk at least 24 kilometers every day to prepare for a multiday hike.On a certain day, Ty plans to walk at an average speed of 4 kilometers per hour. What is the minimum number of hours Ty must walk on that day to fulfill the daily goal?
原库参考解析
线性不等式与可行域基础
A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600 pounds. What is the maximum number of boxes this truck can tow in a trailer with a weight of 500 pounds if each box weighs 120 pounds?
原库参考解析
线性不等式与可行域挑战
y ≤ x ＋7
y ≥ -2x - 1
Which point (x , y ) is a solution to the given system of inequalities in the xy-plane?
原库参考解析
线性不等式与可行域基础
The point (8, 2) in the xy-plane is a solution to which of the fllowing systems of inequalities?
原库参考解析
线性不等式与可行域基础
y >13x - 18
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挑战
y < 6x+ 2
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> 14
4x + y< 18
The point (x, 53) is a solution to the 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
The mininun value of x is 12 less than 6 times another number n.Which inequality shows the possible values of x?
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
A truck can haul a maximum weight of 5,630 pounds. During one trip, the truck will be used to haul a 190-pound piece of equipment as well as several crates. Some of these crates weigh 25 pounds each and the others weigh 62 pounds each. Which inequality represents the possible combinations of the number of 25-pound crates, x, and the number of 62-pound crates, y, the truck can haul during one trip if only the piece of equipment and the crates are being hauled?
原库参考解析
线性不等式与可行域基础
For a snowstorm in a certain town, the minimum rate of snowfall recorded was 0.6 inches per hour, and the maximum rate of snowfall recorded was 1.8 inches per hour. Which inequality is true for all values of s, where s represents a rate of snowfall, in inches per hour, recorded for this snowstorm?
原库参考解析
线性不等式与可行域挑战
y > 4x+8
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
