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挑战
During a portion of a flight, a small airplane's cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where s is the cruising speed, in miles per hour, during this portion of the flight?
原库参考解析
线性不等式与可行域基础
During a portion of a flight, a small airplane's cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where s is the cruising speed, in miles per hour, during this portion of the flight?
原库参考解析
线性不等式与可行域基础
2x - y > 883
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基础
\( y<x \)
\( x<22 \)
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
In a set of four consecutive odd integers, where the integers are ordered from least to greatest, the first integer is represented by x. The product of 12 and the fourth odd integer is at most 26 less than the sum of the first and third odd integers. Which inequality represents this situation?
原库参考解析
线性不等式与可行域进阶
\( y>13x−18 \)
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基础
An event planner is planning a party. It costs the event planner a onetime fee of $35 to rent the venue and $10.25 per attendee. The event planner has a budget of $300. 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基础
The total cost, in dollars, to rent a surfboard consists of a $25 service fee and a $10 per hour rental fee. A person rents a surfboard for t hours and intends to spend a maximum of $75 to rent the surfboard. Which inequality represents this situation?
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基础
The shaded region shown represents the solutions to an inequality. Which ordered pair (x, y) is a solution to this inequality?
原库参考解析
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挑战
\( I=\frac{V}{R} \)
The formula above is Ohmʼs law for an electric circuit with current I, in amperes, potential difference V, in volts, and resistance R, in ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by n six-volt batteries that produce a total potential difference of 6n volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, n, of six-volt batteries that can be used?
原库参考解析
