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
To win a trivia game, a player needs to earn at least 80 total points from responding correctly to questions in two rounds of play. Correct responses in the first round are worth 3 points each, and correct responses in the second round are worth 7 points each. Which inequality represents the situation where the player does not win the game, where \( f \) is the number of correct responses in the first round and s is the number of correct responses in the second round?
参考答案
线性不等式与可行域挑战
A student needs at least 100 signatures from classmates to run for class president. The student collects 60 signatures on Monday and collects enough additional signatures on Tuesday to run for class president. Which inequality represents the number of additional signatures, s, that the student collects on Tuesday?
参考答案
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 \( 7x−4y>28 \)?
参考答案
线性不等式与可行域挑战
A student needs at least 80 signatures from classmates to run for class treasurer. The student collects 55 signatures on Monday and collects enough additional signatures on Tuesday to run for class treasurer. Which inequality represents the number of additional signatures, s, that the student collects on Tuesday?
参考答案
线性不等式与可行域进阶
\( y\ge x+6 \)
\( y\le−3x−6 \)
Which point \( (x,y) \) is a solution to the given system of inequalities in the xy-plane?
参考答案
线性不等式与可行域进阶
\( r+g<40 \)
For which of the following tables are all the values of r and their corresponding values of g solutions to the given inequality?
参考答案
线性不等式与可行域挑战
The minimum value of x is 4 less than 7 times another number n. Which inequality shows the possible values of x ?
参考答案
线性不等式与可行域进阶
To cut a lawn, Jamal charges a fee of $18.00 for his equipment and $8.75 per hour spent cutting a lawn. Sofia charges a fee of $10.00 for her equipment and $10.75 per hour spent cutting a lawn. If x represents the number of hours spent cutting a lawn, what are all the values of x for which Sofia's total charge is greater than Jamal's total charge?
参考答案
线性不等式与可行域挑战
The shaded region shown represents the solutions to which inequality?
参考答案
线性不等式与可行域挑战
The shaded region shown represents the solutions to which inequality?
参考答案
线性不等式与可行域挑战
\( y>13 \)
\( 4x+y<19 \)
The point (x, 48) is a solution to the given system of inequalities in the xy-plane. Which of the following could be the value of x?
\( 4x+y<19 \)
The point (x, 48) is a solution to the given system of inequalities in the xy-plane. Which of the following could be the value of x?
参考答案
线性不等式与可行域挑战
\( y<4x+12 \)
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
参考答案
