Linear inequality word problems pdf The soil cost $4 per bag, and the plants cost $10 each. E Worksheet by Kuta Software LLC 7. Sketch the graphs of linear inequalities. Use the linear inequalities you wrote in part (a) to fi nd the solutions of the absolute value inequality. The problems cover a variety of contexts including loans, population growth, projectile motion, capacity constraints, budgets, and more. Your babysitting job pays $7. Find the numbers. Find important definitions, questions, notes, meanings, examples Graphing Linear Inequalities in Two Variables How to Graph Linear Inequalities in Two Variables: o 1. 1 Equivalent Inequalities Definition 8. Write and graph a system of linear inequalities: b. A linear programming problem consists of an objective function to be optimized subject to a system of constraints. Linear inequalities can be used to model real-world problems. Students can download Grade 7 inequalities worksheets for free in pdf formats and download a variety of inequality questions. y≤ 2 3 x+3 y≥−x x≤2 ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ TOP: 6-5 Problem 3 Graphing a Linear Inequality in One Variable KEY: linear inequality 8. Unit Overview . Unit 5 Notes . x ≥ 13 5. kasandbox. 64 Solve −4≤3x−7<8. ©e B2j0 J121 A lK xu QtHa3 nS Xo 6f 2tEwGaJr7e J tL ALICD. Solutions: Worksheet 11. 12| A. 1 Two inequalities are equivalent if they have the same solution set. For each problem, variables are defined to represent quantities in the problem and 4 possible systems of inequalities are provided as answer choices to model the situation. Units 5 Test Review. Inequalities word problems worksheets helps kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of inequalities. 12 AI. l Z dM Favd Eeh UwfiktTh O uI 8n1f ViOnwiftbe d qAZl9gae Jb5r 1a9 D1 8. Linear Inequalities - Part 1 WS. The first thing to notice about mathematical statements, unlike mathemati-cal expressions, is that astatementmaybetrueorfalse. 339) • intersection (p. b) Solve the inequality to find the maximum number of students in her class. 340) • half-plane (p. 1) y x y x x y Foundations of Math 11: Unit 1 – Linear Inequality Sardis Secondary Foundationsmath11. 6 0 nMnaad5e C Lwji Xtyhr rIZn QfJiOnKiHtRe9 4A 4l cg iepbCrAaX p2 a. define systems of linear inequalities in two variables; 2. Information about Linear inequality word problems covers topics like Linear Inequalities&nbsp; and Linear inequality word problems Example, for SAT 2025 Exam. )A number z is divided by 2 is at least -6 Remember: A solution set is more than one answer, it is all the answers that work in the inequality. 339) • union (p. You’ll be able to check your students' answers quickly and easily with the help of the answer key that’s included, too!We know how busy your lives can be as teachers, which is why we Translating Inequality Phrases Worksheets. H I 1A 6lVlF Cr uilg th Dt0sF Dr9eksTeJr 5vwejdd. ©f 12i0 X1J2 S zK9uOtia x rS 7omfit ewSavr8e W OLSLsCN. . c J cMdapdeeg ]wniNtLhb dI`ngfviknXictVeX ]AMlugjeDbxrmaA p1r. After this, the green line is above the red line. doc / . 50 per hour and your math tutoring job pays $6 per hour. We would like to show you a description here but the site won’t allow us. This is what we will focus on here with some basic number problems, geometry problems, and parts problems. If you're seeing this message, it means we're having trouble loading external resources on our website. Write linear inequalities from graphs. A company’s social committee has $4700 to put towards renting a banquet hall. one for each choice of value for x (or y). 16 0. Students must be familiar with rearranging of inequalities and be able to write inequalities from word problems to choose the best answer. )A number w minus 3 is less than or equal to 10 4. In other words, we may add the same real number to both sides of an inequality, and Describe the values of x + 2 that make the inequality true. 6 and 1. 1 m WAIlFlT hrhisgRhTtRsz Yr2eLsAemrnvPe Sdg. Our Graphing Linear Inequalities in Two Variables Word Problems Worksheet PDF will help your students to practice graphing linear inequalities and includes four word problems for them to have a go at solving. Lesson 1- Solving Problems Involving Linear Inequalities in Two Variables After going through this module, you are expected to: 1. ANS: C PTS: 1 DIF: L2 REF: 6-6 Systems of Linear Inequalities OBJ: 6-6. There are 60 minutes of sewing operator time and 48 minutes of cutter time available. Write and solve an inequality to find out how many additional text messages the teenager can send without exceeding the budget. To write an inequality, look for the following phrases to determine what inequality • Solve a system of linear inequalities in two variables by graphing. ” compound inequality, p. -4-Worksheet by Kuta Software LLCAnswers to 6. 7. 4 on linear inequalities in one variable, we saw apowerfulmethod Free Algebra 2 worksheets created with Infinite Algebra 2. So if we wanted to write the solution to \(x+1>2x-1\), we would say that the solution set is \(x<2\), or all x-values less than 2 (note that we do not include 2 in the solution set since that is the point where the lines are equal). A L 1Mda9d keN 6wsi rt 4hw HINnbf Ti7n niPt ie2 uAjlagte 8b 0r4aL Y1e. 1) She has more than $25. Word Problems. Constraints on the values of x and y that we can choose to solve our problem, will be described by such inequalities. Unit F Part 2 Day 5 Application of Systems of Inequalities Objective: Write an inequality to represent the given situation. PDF: Practice-Solving Linear Equations 2 combining like terms same side: 10: WS PDF: Practice-Solving Linear Equations 3 combining like terms opposite side: 20: WS PDF: Practice-Solving Linear Equations 4 fractional expressions: 15: WS PDF: Practice-Solving Linear Inequalities 1: 10: WS PDF: Practice-Solving Linear Inequalities 2: 10: WS PDF Author: j. Aug 2, 2018 · EXAMPLE 2. Printable PDFs for Inequality Word Problems Worksheets 7th Grade. CED. If the inequality is Q or R, make the line solid. Inequalities Practice Test. 2) The temperature is at least 65 degrees outside. cEXAMPLE 3 System of linear inequalities Solve the system of inequali- If at any point you MULTIPLY OR DIVIDE by a NEGATIVE, you FLIP the inequality Manipulation of MULTI-STEP questions all works the same. x ≥ 1800 calories 4. Admission is $5, and each ride costs $2. use the language of inequalities table to help you select the right inequality; Step 2) Use algebra to solve the word problem Step 3) Rewrite the inequality using algebra. (14 Worksheets) Linear Inequalities Applications Power Point. 5 and 8 3) Flying to Kampala with a tailwind a plane averaged 158 km/h. • Solve problems involving systems of linear inequalities in two variables. 8 Worksheet by Kuta Software LLC Systems of Inequalities A system of linear inequalities consists of two or more linear inequalities that must be satisfied simultaneously. Watch out! You may have to use variables on both sides. b) Solve the inequality. A seafood restaurant owner orders perch and A. 23. We use inequalities to compare two values. w q kAmlJlz nrdiUgbhVtisb Gryefscesrav[eYdV. If the inequality is < or >, make the line dashed. org are unblocked. Here are the 4 main keywords commonly used to write mathematical expressions involving inequalities. REI. x > 21 3. Module MapModule Map This chart shows the lessons that will be covered in this module. 1) y Unit 4: Inequalities Graphing Inequalities One Step Inequalities Two Step Inequalities Multi-Step Inequalities (#1-10 are variables on one side, #11-24 have variables on both sides) Compound Applications of Linear Inequalities (word problems) Compound Inequalities (AND and OR; compound linear inequalities) Quadratic Inequalities (one-variable, solve, plot; FYI: two-variables, graph) Improve your math knowledge with free questions in "Write two-variable inequalities: word problems" and thousands of other math skills. translate statements into mathematical expressions. Linear Inequalities in Two Variables The 5 step problem solving process still applies in solving word problems with inequalities with one exception: Step 1: Read the problem carefully Step 2: Define your variables Step 3: SET UP THE INEQUALITY Step 4: Solve the inequality Step 5: Answer the question Let’s try a few examples: Solving Linear Inequalities Match-Up (Editable Word | PDF | Answers) Graphical Inequalities Worded Problems Grid (Editable Word | PDF | Answers) graph of a system of linear inequalities, and identify possible solutions to systems of linear inequalities with this “Math Lib” Activity. • solve problems using linear programming 2 I am able to • solve problems using linear programming with help 1 I am able to • understand that linear programming involves multiple linear inequalities WARM UP Write a system of inequalities for the shaded region shown in the graph. Linear Inequalities WS. Nov 16, 2022 · Here is a set of practice problems to accompany the Linear Inequalities section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University. Often it takes a bit of practice to convert the english sentence into a mathematical sentence. 3 Day 1 Inequality Word Problems Notes 5 April 16, 2018 Write an inequality to represent the problem. Linear Equations - Word Problems Word problems can be tricky. a. Kuta Software. x < 11 2. 4 and 8 2) The difference of two numbers is 3. Solve! One strategy you can use to find solutions is to graph each inequality. 5. This NO PREP printable worksheet provides step-by-step solutions. 50 per pound. Solving word problems with systems of linear inequalities involves 2 steps: Translate the word problem into mathematical expressions. Write an inequality to determine the minimum number of whole days it will take for him to be able to spell at least 75 words. x ≤ 11 miles 6. 4. You want to spend less than $25 on flour and cornmeal, but you need at least 6 pounds al 2. 1 Solving Systems of Linear Inequalities by Graphing STA: CA A1 9. Linear Equations and Inequalities. The following two examples illustrate techniques for determining the solution set or the graph of such a system. txt) or read online for free. ANS: B PTS: 1 DIF: L3 REF: 6-5 Linear Inequalities OBJ: 6-5. X h xMvayd nez Sw Oi0tNhj HI1nOf2i7nyi0tieu bA 9l3gte xbYrea 7 s2 l. Write an inequality that represents the situation. involving equality) and inequalities (all the rest). They give us an idea of relative size by stating that one is greater, lesser, equal, or not equal to the other value. It becomes essential for us to know how to translate real-life problems into linear inequalities. We're finding a system of linear inequalities. Many times, when we use math, we do not need an exact answer, just an idea if something is going to work. 33 3 (87) > $ , $ > $261 Sun-Li has $30 to spend at the carnival. 9. Use your description to write two linear inequalities that represent the solutions of the absolute value inequality. (14 Worksheets) Linear programming problems are applications of linear inequalities, which were covered in Section 1. • Write inequalities that describe a given situation Inequality worksheets for 7th grade focus on core concepts and thus can be a great guide for grade 7 students. 1 Solving Inequalities With Variables on One Side STA: CA A1 4. Acing the Linear Inequalities and Graphs 61 5-4 Solving Word Problems Using Inequalities 83 Chapter 5 Practice Test 85 Digital SAT Math: Linear inequalities in one or two variables – Practice Questions SAT MAth Practice questions – all topics Algebra Weightage: 35% Questions: 13-15 Master Solving Linear Inequalities with Two Variables through Real-World Modeling Transform your students into masters of solving linear inequalities with two variables using this comprehensive "Linear Inequalities Word Problems" printable PDF worksheet. systems of linear inequalities (A-2-H) (A-4-H) Lesson Focus: This lesson is intended to be an introduction to inequalities and an extension on solving equations. x ≥ 800 hours 7. ©P M2b0t1 F24 8KVuytzaA MSZoUfdtsw2aGrteb 0L1LjC T. Inequalities Word Problems WS. Sutcliffe 5) On earth day, a nursery sold more than $1500 worth of maple and birch trees. Both pants and jackets require the work of sewing operators and cutters. Use compound inequalities to solve real-life problems. A manufacturer of ski clothing makes ski pants and ski jackets. Unit 5 Test Review. A statement involving the symbols ‘>’, ‘<’, ‘ ≥’, ‘≤’ is called an inequality. This document provides examples of writing and graphing systems of linear inequalities to model real-world situations involving two variables. o G tA LlMl1 hr1i fg 1hFt Lsv XrCeAsOe7r jvieZdK. The correct choice is identified for each problem. apply linear inequalities in two variables in real-life situation. o 2. Systems of Inequalities: Word Problems 6. 82 Core VocabularyCore Vocabulary The graph of a compound inequality with “and” is the intersection Aug 20, 2024 · Solutions to linear inequalities represent a region of the Cartesian plane. 319) • compound inequality(p. 1. weebly. Peter begins his kindergarten year able to spell 10 words. 4 Linear Inequalities and Problem Solving 79 Addition Property of Inequality If a, b, and c are real numbers, then a 6 b and a + c 6 b + c are equivalent inequalities. She wants to buy at least 5 plants and can spend no more than $100. q Worksheet by Kuta Software LLC Solving Systems of Inequalities Date_____ Period____ Sketch the solution to each system of inequalities. Be sure to define your variable. 0 TOP: 6-6 Example 1 KEY: linear inequality | graphing | system of linear inequalities | graphing a system of linear inequalities 19. Graph the solution on a number line. Graph the solution to this system of inequalities on the set of axes below. 8 A system of inequalities is graphed on the set of axes below. 2) More than 450 students went on a field trip. Day #2 - Writing Inequalities From Word Problems I varied how I used the worksheets, depending on the ability of my students. The cost to rent a banquet hall is $500, plus $35 per person. By understanding the real situation, we have to use two variables to represent each quantities Problem 1 : When writing an inequality from a word problem, there are two simple steps you need to follow Step 1) Read the word problem carefully and change the word problem into algebra. 84 10-6 Dividing Monomials. bolla Created Date: 12/23/2016 8:21:10 AM To solve word problems using linear inequalities, we have to model the information given in the question as linear inequalities and solve for unknown. Suppose you buy flour and cornmeal in bulk to make flour tortillas and corn tortillas. Solving a Linear Inequality Word Problem Example. Lesson/Title Page 10-5 Multiplying Monomials. com Mr. After buying them she had $10. 3) You will need at most 4 pieces of paper to do the assignment. Age problems are common applications that you will see when solving linear inequality word problems. Then, use the overlapping areas of the graphs to identify the solutions to the word Solving Linear Equations and Inequalities in One Variable After going through this module, you are expected to: 1. 3 Sketch the solution to each system of inequalities. By the end of this lesson students should know the following: • The meaning of inequality sentences involving <, >, <, and >. Inequality Word Problems 12w > 530, w > 44. Test a point in one half plane created. Units 4 and 5 Test Review. Lesson 2– Solving Problems Involving Systems of Linear Inequalities in Two Variables After going through this module, you are expected to: 1. B. Activity Directions: Print and post the ten stations around the ©l h2u0g1g8w VK]uXtSal `SeoFfTtxwiaArAeV oLCLfCY. 75x > 55, x > 73. d TOP: 6-5 Problem 3 Graphing a Linear Inequality in One Variable KEY: linear inequality 9. Operations that Produce Equivalent Inequalities. A quadratic inequality in two variables can be written in one of the following forms, where a, b, and c are real numbers and a ≠ 0. He is going to learn to spell 2 new words every day. docx), PDF File (. Mar 28­2:47 PM You can work a total of no more than 10 hours each week at your two jobs. The constraints are a system of linear inequalities that represent certain restrictions in the problem. This will present some problems from the point of view of solving such equations—finding all solutions. Six buses were filled and 7 students traveled in cars. 3| CC A. D. kastatic. In this part of our two-step inequalities pdf worksheets, grade 7 and grade 8 students get adequate practice in setting up a two-step inequality by translating verbal descriptions of real-life scenarios. x ≤ 34 students a) Choose a variable and write an inequality for this problem. Systems of Linear Equations and Inequalities in Two Variables Systems of Linear Equations in Two. 1) 8. 1 Solving Systems of Linear Inequalities by Graphing To solve some optimization problem, speci cally linear programming problems, we must deal with linear inequalities of the form ax+ by > c ax+ by 6 c ax+ by > c ax+ by < c; where a, b and c are given numbers. Write a system of linear inequalities to model the situation. c 0 UA Xljlz aroi1g6h jtEs3 Zrueas 3e yr6voeDd7. Their sum is 13. On the return trip the plane only ©j M230g1 q1C QK8uWtKaB CSQovfWt0w ka9r TeY 0LlLFCg. How many students were in each bus? 2) Aliyah had $24 to spend on seven pencils. What is the greatest numbe r of rides she can ride? Additional Example 2: Application 5 + 2r ≤30 – 5 –5 2r ≤25 2r ≤25 2 2 Subtract 5 from both sides. Inequalities word problems worksheets are also helpful for students to prepare for various competitive exams. For example, a linear inequality can be used to model the distance that a car with given fuel-economy ratio can be driven using no more than twenty-two gallons of gasoline. solve problems involving systems of linear inequalities in two variables. How much did each pencil cost? 3) The sum of three consecutive numbers is 72. -1- ©L B2Q0A1Y1c lK nu 0tTa v 6SVohfEt vwvabrre O HLbL 9CT. 50 per pound and cornmeal costs $2. They must use inequality symbols like <, >, ≤ or ≥ according to the phrases used in the sentences and quickly translate them. b) Solve the inequality to find the minimum number of people on each bus. The key elements are to understand the context of each problem, identify the relevant variables, and write an appropriate linear inequality to model the relationship between variables and KEY: Multiplication Property of Inequality for c > 0 | problem solving | word problem | solving inequalities | multi-part question 15. Inequalities Word Problems Guided Notes. To turn the English into Algebra it helps to: Read the whole thing first; Do a sketch if needed; Assign letters for the values; Find or work out formulas Inequalities can be manipulated like equations and follow very similar rules, but there is one important exception. Writing and Graphing Compound Inequalities A compound inequality is an inequality formed by joining two inequalities with the word “and” or the word “or. Previously, you graphed linear inequalities in two Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and child tickets, y, that would satisfy the cinema's goal. You need to earn at least $85 to cover your gas and food expenses. 3. If you're behind a web filter, please make sure that the domains *. )Twice the number p is fewer than 7 3. 2. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer. Unit 5 Constructed Response Test Review . a) Write an inequality to represent the situation. PDF DOC: Regents-Modeling Systems of Linear Inequalities AI/AI: 1/9: TST PDF DOC: PRACTICE WORKSHEETS: Practice-Modeling Linear Systems 1 ratio: 10: WS PDF: Practice-Modeling Linear Systems 2 mixed: 17: WS PDF: Practice-Modeling Linear Systems 3 break even: 10: WS PDF: Practice-Modeling Systems of Linear Inequalities: 9: WS PDF: LESSON PLANS hour. The document contains 23 word problems involving linear inequalities. find the solution of linear equation or inequality in one variable; 2. )A number n is greater than 1 2. 1 To graph linear inequalities in two variables NAT: CC A. Units 4 and 5 Linear inequalities can be simple (x<3) or complex (3x+2≤½−14x), and can arise naturally in the real world so — you guessed it — word problems! • Equivalent Inequalities • Linear and Nonlinear Inequalities • Absolute Value Inequalities (Sections 4. The profit on a pair of ski pants is $2. Simplify. If you subtract the same number from both sides of the inequality, the inequality remains true. Multiple Choice (80 points, 5 points each) Identify the choice that best completes the statement or answers the question. solve problems involving linear inequalities in two variables; and 3. C. 0 TOP: 3-4 Example 2 KEY: solving inequalities | problem solving Systems of Equations Word Problems Date_____ Period____ 1) Find the value of two numbers if their sum is 12 and their difference is 4. solve linear equation or inequality in one variable involving absolute value by: (a) graphing; and (b) algebraic methods; and, 3. Write linear inequalities. Math 7th Grade Inequalities Worksheet OBJ: 6-6. The club sells 144 cans of lemonade. Just don’t forget to FLIP the inequality when every time you multiply or divide by a NEGATIVE. In other classes, I gave them all the problems and let them choose a certain number to complete. Writing Linear Inequalities An inequality is a mathematical sentence that compares expressions. 85 10-7 Powers of Monomials. b. In some classes, I gave out the more challenging problems to the students who needed it. Module MapModule Map Here is a simple map of the lessons that will be covered in this module. 353) Inequalities are used to represent various real-world situations in ISBN 978-0-9754753-6-2 PDF. Solution Add 7 to all three parts. Considering texts sent must be positive, 0 ≤ t ≤ 200. Jaden is buying plants and soil for her garden. I was reminded of this concept this very STANDARD A. Solve applications of linear systems of inequalities. Linked in here are our printable translating inequality phrases worksheets that allow students to translate sentences into inequalities with swagger. Write a system of linear inequalities to model the situation and then solve. 2 Graphing linear equations in two variables In Section 4. Two-Variable Linear Inequalities Word Problems - Free download as PDF File (. Printable in convenient PDF format. An inequality contains the symbol <, >, ≤, or ≥. Learn how to solve linear inequality word problems for the SAT with step-by-step explanations and practice exercises. 00 and on a jacket is $1. It takes 8 minutes Section 2. Linear Inequalities Part 2 WS. The document presents 6 word problems involving systems of linear inequalities. How many people could attend the function if they rented the banquet hall? a) Choose a variable and write an The worksheets on this page require kids to solve inequalities by graphing. How many tickets do they need to sell? Justify your answer. You can work at most 25 hours next week. ANS: C PTS: 1 DIF: L4 REF: 3-4 Solving Multi-Step Inequalities OBJ: 3-4. • Add or Subtract the same value on both sides of the inequality. graph systems of linear inequalities in two variables; and 3. ] v uAilJlN FrziMgRh_tjsC AryedsLeJr_vEejd]. The worksheet attached below will provide you with some practice using number lines to communicate your answers to inequality word problems. Flour costs $1. SOLVING SYSTEMS OF LINEAR INEQUALITIES . 1. The basic inequalities < and > are called strict inequalities, while the compound inequalities ≤ and ≥ are sometimes called non-strict inequalities. Systems of Linear Inequalities Word Problems - Free download as Word Doc (. Ten buses were filled and 5 more students traveled in a car. y < ax2 + bx + c y > ax2 + bx + c y ≤ ax2 + bx + c y ≥ ax2 + bx + c The graph of any such inequality consists of all solutions (x, y) of the inequality. • illustrate linear inequalities in two variables; • graph linear inequalities in two variables on the coordinate plane; and • solve real-life problems involving linear inequalities in two variables. Writing and solving word problems involving them helps develop our problem-solving approach, understanding, logical reasoning, and analytical skills. R 4 VAclTls 6r9i Og5h 9tOs3 2r1e PsBevrMvUeYde. Let t represent the number of additional text messages beyond the allowance. Translating Inequality Phrases Worksheets. A few important phrases are described below that can give us clues for how to set The notes and questions for Linear inequality word problems have been prepared according to the SAT exam syllabus. Apr 17, 2024 · They help us express relationships between quantities that are unequal. Change the inequality sign to an equal sign, then plot the line. 50. 86 inequalities that can be used to represent this situation. Linear Inequalities Before defining the linear inequalities formally, let’s see them through a real-life situation and observe why their need arises in the first place. org and *. pdf), Text File (. 316 Chapter 6 Solving Linear InequalitiesSolving Linear Inequalities Solving Linear Inequalities Key Vocabulary • set-builder notation (p. If you add the same number to both sides of an inequality, the inequality remains true. Example 4: Solve for the unknown in the equation: − u R s t Solution 4: − u − u R s t − u Q− v • PRACTICE PROBLEMS: Write the word sentence as an inequality. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Forexample,1+2=3 Worksheet by Kuta Software LLC Algebra 2 Practice 4. Divide each part by three. 0 | CA A1 5. Graph the solution and write the solution in interval notation. H Worksheet by Kuta Software LLC Inequality Word Problems Worksheets. Problem 1 : Find all pairs of consecutive odd positive integers, both of which are smaller than 18, such that their sum is more than 20. While the inequalities are directly given in some worksheets, some have word problems that require you to frame them. c. 2 1. 4--Systems of Inequalities (Word Problems)--EXAMPLES ©E L2N0y1N5s [K[uOthar kSloofMtLwtalrJeY TLqLyCq. Q Worksheet by Kuta Software LLC As you can see, the red line is above the green line as long as \(x<2\). Two-Step Equation Word Problems Date_____ Period____ 1) 331 students went on a field trip. State the system of inequalities represented by the graph. V D 1M 6a 7d Dej 1wti 1t QhQ vIntf yi Dn5i qt 5e6 CAEl5g Pejb ur Xad 82Y. Porter is going to the store to buy Turning English into Algebra. 4 Practice - Solving Linear Inequalities 1) x 2) x 3) n 4) b 5) x 6) r 7) x : Linear Programming Word Problems 1. cbzxr bomg iqy xlbis lvvs xribzf ldmnd taqa dkau kekizyf jugk yymmz faxk vbjg wtmibo