5 See WORKED-OUT SOLUTIONS Exs. 11, 23, and 45 5 STANDARDIZED TEST PRACTICE Exs. 2, 32, 44, 48, and s 5 } 11. 3p ,

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1 . EXAMPLES,, and for Es. EXAMPLE for Es. EXAMPLE for Es. 6 EXERISES SKILL PRATIE A. The absolute value smbol was removed without writing the second equation, ; 9 or.. The absolute value of a number is never negative, so it is incorrect to rewrite this absolute value equation as two equations; there are no solutions.. VOABULARY op and complete: The equation. is an eample of a(n)?. absolute value equation. WRITING Given 9, describe the relationship between, 9, and using absolute deviation. The absolute deviation of from 9 is. SOLVING EQUATIONS Solve the equation. HOMEWORK KEY See WORKED-OUT SOLUTIONS Es.,, and STANDARDIZED TEST PRATIE Es.,,, 8, and 9.,. 6 6, 6. v..,. 6. w 9. 9., 9.. r 8. s,, 9. m,. n 8. p,,. q 8 6,. d, 9. f 8, 6. t 6. b. c, 9, 8, 8. j, 9. k 6. g 6 9,, ERROR ANALYSIS Describe and correct the error in solving the absolute value equation or 6 9 or 8 SOLVING EQUATIONS Solve the equation, if possible m. no solution no solution., n. v 9 8., 6 w 6, no solution 9. r. s 8. 9 p 8, no solution,. MULTIPLE HOIE Which number is a solution of? D A B D There is no solution. USING ABSOLUTE DEVIATION Find the values of that satisf the definition of absolute deviation for the given value and the given absolute deviation.. Given value: ;. Given value: ; absolute deviation: 8, absolute deviation:,. Given value: 9.; 6. Given value:.; absolute deviation:.6.,. absolute deviation: 6..,. PRATIE and APPl Assignment Guide Answers for all eercises available online Basic: Da : Es. Da : Es., Average: Da : Es.,, 6, Da : Es. 6, 9 Advanced: Da : Es.,, 6 8,, * Da : Es. 6, * Block: Es.,, 6, (with previous lesson) Es. 6, 9 (with net lesson) Differentiated Instruction See Differentiated Instruction Resources for suggestions on addressing the needs of a diverse classroom. Homework heck For a quick check of student understanding of ke concepts, go over the following eercises: Basic:,, 6,, Average: 6,,, 6, Advanced: 8,,,, Etra Practice Student Edition hapter Resource Book: Practice levels A, B, Differentiated Instruction Below level Some students ma need help in determining whether the can solve Eercises. Demonstrate strategies the can use to determine whether the absolute value equation is equal to a negative number and, thus, has no solution. In Eercise, point out that the right side becomes 6 8, and in Eercise 6, point out that the right side becomes. Have students use these strategies to identif all the eercises that have no solutions. See also the Differentiated Instruction Resources for more strategies.. Solve Absolute Value Equations Practice Worksheet An easil-readable reduced practice page can be found at the beginning of this chapter.

2 Avoiding ommon Errors Eercises Watch for students who tr to solve these equations without rewriting them in the form a b c. Remind them that the absolute value epression must be equal to a nonnegative number before the can rewrite it as two equations. Mathematical Reasoning Eercise Students should know that b means is b units from on the number line. You ma want to ask them to interpret b as a middle step in understanding that a b means is b units from a. B EXAMPLE A for Es. 6. SOLVING AN EQUATION Interpreted geometricall, the equation a b means that the distance between and a on a number line is b. Solve both geometricall and algebraicall. ompare our solutions. The distance between and is,, ; or,, ; the solutions are the same. TRANSLATING SENTENES In Eercises 8 and 9, write the verbal sentence as an absolute value equation. Then solve the equation. 8. Four more than the absolute deviation of from is 8. 8;, 9. Five times the absolute deviation of from 9 is.. REASONING Is a equivalent to a when a is positive? when a is negative? when a is? Give eamples to support our answers. See margin.. HALLENGE How man solutions does the equation a b c d have if a > and c d? if a < and c > d? one, two PROBLEM SOLVING 9 ;, 6. GUARDRAILS A safet regulation requires that the height of a guardrail be inches with an absolute deviation of inches. Find the minimum and maimum heights of a guardrail. 9 in., in.. Yes; no; es; when a and, () 6 6 () ; when a and, () 6 Þ 6 () ; when a and, ().. HEERLEADING A cheerleading team is preparing a dance program for a competition. The program must last minutes with an absolute deviation of seconds. Find the least and greatest possible times (in seconds) that the program can last. sec, sec. MULTIPLE HOIE The diameter of a billiard ball must be. inches with an absolute error of. inch. What is the maimum possible diameter that a billiard ball can have? A. inches B. inches. inches D. inches 6. SPORTS In gmnastics meets last ear, the mean of our friend s least and greatest scores was.6 points. The absolute deviation of his least and greatest scores from the mean was. points. a. What were the least and greatest scores that he earned?.6 points, points b. This ear the mean of his least and greatest scores is 6.8 points, and the absolute deviation of the least and greatest scores from the mean is. point. How man points more than last ear s greatest score is this ear s greatest score?. point 6. JEWELRY A jewelr store advertisement states that a certain diamond bracelet weighs carats, but the actual weight can var b as much as % of the advertised weight. Find the minimum and maimum possible weights of the bracelet. See WORKED-OUT SOLUTIONS in Student Resources STANDARDIZED TEST PRATIE. carats,.6 carats Patrik Giardino/orbis 6

3 B 9b. Yes; make a table of values for (m, p) using integer values of m from to 8. Look for the lowest value of p in the table.. ONTESTS You currentl have points in an academic contest. You choose the value p of the question ou want to answer. The value p represents the absolute deviation of our new score s from. a. Write an absolute value equation that gives p in terms of s. p s b. If ou choose a question worth points, what are the possible new scores that ou can have after answering the question? points, 6 points 8. EXTENDED RESPONSE The percent p of United States residents who were foreign born, or born outside of the United States, during the period 9 can be modeled b the equation p.6 t 6.8 where t is the number of ears since 9. a. Approimate During the period 9, in approimatel what ear did foreign-born residents account for % of all residents? 9 b. Predict If the model holds for ears after, predict the ear in which foreign-born residents will again account for % of all residents. c. Decide According to the model, did foreign-born residents account for % of all residents at an time during the period 9? Eplain our answer. No; if ou substitute for p in the model, the equation has no solution. 9. SHORT RESPONSE A stock s average price p (in dollars) during the period Februar to October can be modeled b the equation p. m 9. where m is the number of months since Februar. a. Approimate In approimatel what month and ear was the average price $6.? If the model holds for months after October, predict the month and ear in which the average price will again be $6.. June ; November b. Justif Is it possible to use the model to estimate the stock s lowest average price during this period? Justif our answer.. HALLENGE In a recent Olmpics, swimmers in a men s meter butterfl event finished with times from minute. seconds to minute.8 seconds. Let t represent the slowest or fastest time (in seconds). Write an absolute value equation that describes the situation. t.6. ASSESS and REtEAch Dail homework Quiz Also available online Solve the equation, if possible.. 9,. no solutions. 6,. no solutions. A pattern for a 6-inch skirt allows for an absolute deviation of. inches. Find the minimum and maimum skirt lengths that can be made from the pattern. minimum:. in.; maimum:. in. Online Quiz Available at m.hrw.com Diagnosis/Remediation Practice A, B, in hapter Resource Book Stud Guide in hapter Resource Book Practice challenge Additional challenge is available in the hapter Resource Book. See EXTRA PRATIE in Student Resources ONLINE QUIZ at m.hrw.com

4 .6 EXAMPLES,, and for Es. EXERISES SKILL PRATIE A. When the inequalit has the absolute value epression isolated on the left side, the equivalent compound inequalit will use and if the smbol is < or, and it will use or if the smbol is > or.. The compound inequalit should use or: > or < ; > 9 or <. B. Part of the compound inequalit is missing; the compound inequalit should be < < ; < <.. VOABULARY op and complete: The inequalities > 8 and > 8 or < 8 are?. equivalent inequalities. WRITING Describe the difference between solving and solving. Solving involves solving a compound inequalit with and, while solving involves solving a compound inequalit with or. SOLVING INEQUALITIES Solve the inequalit. Graph our solution.. See margin for art.. < < <. or. h >. h <. or h >. 6. p <.. < p <.. t 8. j t j or j 9. d d or d. b < < b <. m > 6 m < 8 or m >. s < < s <. c c or c. 9 n n.. HOMEWORK KEY r > r < 8 or r > 6. s 8 >. u s < or s > 8 u 8. w 8 < 9. v >. or u 6 f 6 < w < v < 6 or v > f or f 9. MULTIPLE HOIE Which inequalit is equivalent to < or >? B A 8 > B 6 > 9 < D 9 < 8. WRITING How can ou tell whether an absolute value inequalit is equivalent to a compound inequalit with and or to a compound inequalit with or? ERROR ANALYSIS Describe and correct the error in solving the inequalit... > > > 9 > > < < < TRANSLATING SENTENES Write the verbal sentence as an inequalit. Then solve the inequalit and graph our solution. 8. See margin for art.. The absolute deviation of from 6 is less than or equal to. See WORKED-OUT SOLUTIONS Es. 9,, and STANDARDIZED TEST PRATIE Es.,,,, and MULTIPLE REPRESENTATIONS E. 8 6 ; 6. The absolute deviation of from is greater than or equal to. ; or. Three more than the absolute deviation of from is greater than. > ; <. or > 8. Four times the absolute deviation of from 9 is less than 8. 9 < 8; < < PRATIE and APPl Assignment Guide Answers for all eercises available online Basic: Da : SRH p. SR, Es. Es.,, odd, 8, 8 Average: Da : Es.,, 6 even,, odd, Advanced: Da : Es., 6 even,,, 6 even, *, *, 6 * Block: Es.,, 6 even,, odd, (with previous lesson) Differentiated Instruction See Differentiated Instruction Resources for suggestions on addressing the needs of a diverse classroom. Homework heck For a quick check of student understanding of ke concepts, go over the following eercises: Basic:,,,, Average: 6,, 8,, 6 Advanced: 8,,, 8, Etra Practice Student Edition hapter Resource Book: Practice levels A, B, Practice Worksheet An easil-readable reduced practice page can be found at the beginning of this chapter..6 Solve Absolute Value Inequalities. _MESE68_L6.indd 6 6. npe-sa66-9-t nan-66--t nan-66--t 9 nan-66--t //::6 AM nan-66--t nan-66--t nan-66--t 9 nan-66-8-t

5 Avoiding ommon Errors Eercises 9 Some students ma switch and and or when the rewrite absolute value inequalities. Remind students that a b < c and a b c are rewritten using and and that a b > c and a b c are rewritten using or. Mathematical Reasoning Multiple Representations Eercise 8 You ma want to discuss the advantages of using tables to organize data. Stress that presenting numbers in tables allows students to find the data the need quickl. Suggest the create a table that has three colunns with a title at the top of each, such as minimum, p, and maimum. The can also use the top of each column to indicate the calculation the need to perform. Graphing alculator Eercise 9 Students can use a graphing calculator to calculate the mean. The should use the STAT option, then EDIT, and enter the data in the list. After the enter the data, the should go to STAT, then AL, and then choose -VAR stats and the list number, such as L. This will produce a screen that includes the mean. Internet Reference Eercise For more information about pronghorn antelope, visit htm 8a. See Additional Answers.. 6 < < ; solve each absolute value inequalit b rewriting it as a compound inequalit. Graph the solutions and find the intersection of the graphs. EXAMPLE A for Es. 8 REASONING Tell whether the statement is true or false. If it is false, give a countereample. 9. If a is a solution of 8, then a is also a solution of 8. true. If a is a solution of > 8, then a is also a solution of > 8. False. Sample answer:. If a is a solution of 8, then a is also a solution of 8. False. Sample answer:. If a is a solution of 8, then a is also a solution of 8. true. HALLENGE Solve < and > 8. Describe our steps.. HALLENGE If a b < c where c <, what is the solution of the inequalit? If a b > c where c <, what is the solution of the inequalit? Eplain our answers. No solution; all real numbers; because an absolute value cannot be negative, for an real number, a b is nonnegative, so if c is a negative number, a b > c for an real number. PROBLEM SOLVING. ESSAY ONTEST An essa contest requires that essa entries consist of words with an absolute deviation of at most words. What are the possible numbers of words that the essa can have? at least words and at most words 6. SWIMMING POOL The saturation inde for a pool measures the balance between the acid level and the amount of minerals in pool water. Balanced water has an inde value of. Water is highl corrosive or highl scale forming if the absolute deviation of the inde value from is greater than.. Find the inde values for which pool water is highl corrosive or highl scale forming. greater than. or less than.. SHORT RESPONSE You are preheating an oven to 8F before ou bake muffins. Several minutes later, the oven thermometer reads 68F. The measured temperature has an absolute deviation of at most 8F. Write and solve an inequalit to find the possible temperatures in the oven. Should ou continue to preheat the oven, or should ou start baking the muffins? Eplain our choice. t 6, at least 8F and at most 88F; continue to preheat; the temperature is still below 8F. 8. MULTIPLE REPRESENTATIONS Softball compression measures the hardness of a softball and affects the distance that the softball can travel upon contact with a bat. A softball organization requires that the compression of a softball be pounds but allows an absolute deviation of at most pounds. a. Making a Table Make a table that shows the absolute deviation from the required compression when the measured compression of a softball is p pounds. Use the following values for p:,,,,. See margin. b. Writing an Inequalit Write and solve an inequalit to find the softball compressions that the organization will allow. Which values of p in the table are solutions of the inequalit? p, at least lb and at most lb;, See WORKED-OUT SOLUTIONS STANDARDIZED in Student Resources TEST PRATIE Differentiated Instruction MULTIPLE REPRESENTATIONS Visual Learners Students probabl understand that acceleration means an increase in velocit, but ma be confused b the mathematical notation. In Eercise 9, an acceleration of m/sec means a velocit of meters per second in second, a velocit of meters per second in seconds, and so on. Have m students write acceleration as m sec per sec or sec sec. Show m that this is equal to sec. See also the Differentiated Instruction Resources for more strategies. Michael Newman/PhotoEdit

6 B b. p 8, 6; at least, antelope and at most,6 antelope. 9. MULTI-STEP PROBLEM In a phsics class, groups of students eperimentall determine the acceleration (in meters per second per second) of an object in free fall. The table below shows the value calculated b each group. Group 6 alculated value (m/sec ) a. alculate Find the mean of the measured values given in the table. Round to the nearest hundredth.. m/sec b. Solve When writing up their lab reports, the students wanted to state that the absolute deviation of each measured value from the mean was at most d. What is the value of d in this situation?.88 m/sec. EXTENDED RESPONSE Relative absolute deviation of a number from a given value is the absolute deviation epressed as a percent of the given value. A wildlife biologist estimates that the number of pronghorn antelope in Nevada is 8, with a relative absolute deviation of at most %. a. alculate Find the absolute deviation from the estimated population of pronghorn antelope b multipling the estimated population b the relative absolute deviation. 6 antelope b. Solve Write and solve an inequalit to find the possible numbers of pronghorn antelope in Nevada. c. Eplain If the relative absolute deviation were %, could ou conclude that the actual population is necessaril greater than if the relative absolute deviation were %? Eplain our reasoning. See margin.. HALLENGE According to the rules for a women s figure skating event, a skater should finish a routine in an ideal time of minutes seconds. The skater receives a. point penalt if the absolute deviation of the finishing time from the ideal time is greater than seconds and less than or equal to seconds. Write and solve an inequalit to find the finishing times for which the skater receives a. penalt point. at least minutes seconds and less than minutes seconds, more than minutes seconds and at most minutes seconds ASSESS and REtEAch Dail homework Quiz Also available online Solve the inequalit. Graph our solution.. > all real numbers less than or greater than all real numbers greater than or equal to and less than or equal to 6. The clock in our car has an absolute deviation of at most minutes after 6 months. After 6 months, the clock reads :8. Write and solve an inequalit to find the possible times. :8 ; from : through : Online Quiz Available at m.hrw.com Diagnosis/Remediation Practice A, B, in hapter Resource Book Stud Guide in hapter Resource Book Practice challenge Additional challenge is available in the hapter Resource Book. D. Robert & Lorri Franz/orbis See EXTRA PRATIE in Student Resources ONLINE QUIZ at m.hrw.com c. No; if the relative absolute deviation is %, then the actual population is between, and, antelope. For the % relative absolute deviation the actual population might be, antelope, which is less than an possible actual population for the % relative absolute deviation.

7 . EXAMPLE for Es. EXAMPLES,,, and for Es. 6 8 EXERISES SKILL PRATIE A. VOABULARY op and complete: The ordered pair (, ) is a(n)? of >. solution. WRITING Describe the difference between graphing a linear inequalit in two variables and graphing a linear equation in two variables. See margin. HEKING SOLUTIONS Tell whether the ordered pair is a solution of the inequalit.. < ; (, ). ; (8, ). > ; (, ) not a solution solution not a solution 6. ; (, ). > 8; (, ) 8. < ; (, 6) solution not a solution solution ; (, )... >.; (6, ). ; (, ) solution not a solution not a solution. 8; (9, ). < 6; (8, ). ; (, ) solution solution solution. MULTIPLE HOIE Which ordered pair is not a solution of <? A (, ) B (, ) (, ) D (, ) 6. MULTIPLE HOIE The graph of which inequalit is shown? A A B D GRAPHING INEQUALITIES Graph the inequalit. 6. See margin.. > <. 8. < > 6.. ( ) > 6. < () 9. <.. >.. ( ) > 8. ( 6). HOMEWORK KEY See WORKED-OUT SOLUTIONS Es., 9, and STANDARDIZED TEST PRATIE Es.,, 6, 9, 6, 9, and 6 MULTIPLE REPRESENTATIONS E. ( ) < 8 6. ( ) ERROR ANALYSIS Describe and correct the error in graphing the inequalit., 8. See margin for art.. 8. The wrong half-plane is shaded. The boundar line should be solid.. Graph Linear Inequalities in Two Variables PRATIE and APPl Assignment Guide Answers for all eercises available online Basic: Da : Es., Da : Es. 9, 8 Average: Da : Es.,, 8 6, 8, 6 Da : Es. 9,, 9 Advanced: Da : Es., 6, 8, 6, *, * Da : Es. 9,, 6* Block: Es.,, 8 6,, 9 Differentiated Instruction See Differentiated Instruction Resources for suggestions on addressing the needs of a diverse classroom. Homework heck For a quick check of student understanding of ke concepts, go over the following eercises: Basic:, 8,,, Average:,,,, Advanced:,, 8,, Etra Practice Student Edition hapter Resource Book: Practice levels A, B, Practice Worksheet An easil-readable reduced practice page can be found at the beginning of this chapter.. Graphing a linear inequalit in two variables involves graphing the boundar line (as either a solid or dashed line) and then shading the appropriate half-plane. Graphing a linear equation in two variables involves onl the graphing of one (solid) line. 8. See Additional Answers.

8 9. WRITING an ou use (, ) as a test point when graphing >? Eplain our reasoning. No; (, ) is a point on the boundar line. Avoiding ommon Errors Eercises 6 Some students ma test a point on the boundar line. Remind students that a point on the boundar line cannot be used to determine which half-plane to shade. B TRANSLATING SENTENES Write the verbal sentence as an inequalit. Then graph the inequalit.. See margin for art.. Four less than is greater than or equal to.. The product of and is less than or equal to the sum of and The quotient of and is greater than the difference of and. >. The sum of and the product of and is less than. < Graphing alculator Eercises 6 Students ma want to check the boundar lines using a graphing calculator. The should use the = ke, enter the equation, and then select GRAPH.. >. 9 USING A GRAPH Write an inequalit of the graph shown.. (, ). (, ) (6, ) 6. (, ) (, ) Teaching Strateg Eercises 6 Before assigning these eercises, ou ma want to review how to write a linear equation given two points. Remind students to choose an inequalit smbol b looking at whether the boundar line is solid or dashed and b observing which half-plane is shaded.. 6. > (, ) WRITING INEQUALITIES Write an inequalit whose graph contains onl the points in the given quadrants.. Quadrants I and II > 8. Quadrants II and III < 9. Quadrants III and IV <. Quadrants I and IV > HALLENGE In Eercises and, write and graph an inequalit whose graph is described b the given information.,. See margin for art.. The points (, ) and (, ) lie on the boundar line. The points (6, ) and (, ) are solutions of the inequalit.. The points (, 6) and (, 8) lie on the boundar line. The points (, ) and (, ) are not solutions of the inequalit. < PROBLEM SOLVING. 6 EXAMPLE 6 A for Es.. BOBSLEDS In a two-man bobsled competition, the sum of the weight (in pounds) of the bobsled and the combined weight (in pounds) of the athletes must not eceed 86 pounds. Write and graph an inequalit that describes the possible weights of the bobsled and the athletes. Identif and interpret one of the solutions.. > See margin.. ELEVATORS The number of passengers riding an elevator can be no greater than the elevator s maimum weight capacit (in pounds) divided b. Write and graph an inequalit that relates the number of passengers to the maimum weight capacit. Identif and interpret one of the solutions. See margin. See WORKED-OUT SOLUTIONS in Student Resources STANDARDIZED TEST PRATIE MULTIPLE REPRESENTATIONS Paul J. Sutton/Duomo/orbis... < <

9 B 9a., see margin for art. Sample answer: (, ), (, ), (6, ) 9b. Yes; no; (, ) means that ou do not take a duffel and have a pound bedroll, while (, ) means ou take a pound duffel and do not take a bedroll. You need to bring both a duffel and a bedroll.. MULTIPLE REPRESENTATIONS You tutor Spanish for $ per hour and French for $ per hour. You want to earn at least $ per week. a. Writing an Inequalit Write an inequalit that describes our goal in terms of hours spent tutoring Spanish and hours spent tutoring French. b. Drawing a Graph Graph the inequalit. Then give three possible combinations of hours that meet our goal. See margin. c. Making a Table Make a table that gives the amount of mone that ou will earn for each combination of hours given in part (b). See margin. 6. MULTIPLE HOIE To compete in a piano competition, ou need to perform two musical pieces whose combined duration is no greater than minutes. Which inequalit describes the possible durations and (in minutes) of the pieces? B A < B > D. MULTI-STEP PROBLEM You are making muffins and loaves of bread for a bake sale. You need 6 batch of batter per muffin and batch of batter per loaf of bread. You have enough ingredients to make up to batches of batter. 6 m l ; See margin for art. a. Write and graph an inequalit that describes the possible combinations of muffins m and loaves l of bread that ou can make. b. You make loaves of bread. What are the possible numbers of muffins that ou can make? m 6 8. NUTRITION A nutritionist recommends that the fat calories consumed per da should be at most % of the total calories consumed per da. a. Write and graph an inequalit that relates the number of fat calories consumed to the total calories consumed..; see margin for art. b. Use the nutrition labels below. You normall consume calories per da. So far toda ou have eaten 6 crackers and container of ogurt. What are the possible additional fat calories that ou can consume toda? 9. SHORT RESPONSE You need to bring a duffel and a bedroll for a trip in the mountains. The sum of the weight (in pounds) of the duffel and the weight (in pounds) of the bedroll cannot eceed pounds. a. Graph and Appl Write and graph a linear inequalit that describes the possible weights of the duffel and bedroll. Then give three possible combinations of weights of the duffel and bedroll. See margin. b. Interpret Are (, ) and (, ) solutions of the inequalit in part (a)? Do these ordered pairs make sense for this situation? Eplain.,. See Additional Answers.. Graph Linear Inequalities in Two Variables Stud Strateg Eercise Suggest that students review Eample 6 before the begin this eercise. This will help them write a verbal model for the problem, graph the inequalit, and create a table. b. French (hours) Spanish (hours) c. Sample answer: Spanish time (hours) French time (hours) Total earnings (dollars) a. 8a. 9a. Number of loaves of bread Fat calories Bedroll weight (pounds) 6 8 l m l m Number of muffins 6. Total calories Duffel weight (pounds)

10 ASSESS and REtEAch Dail homework Quiz Also available online Tell whether the ordered pair is a solution of the inequalit.. 6; (, ) no. < ; (, ) es. For a fundraiser, students offer a basic car wash for $ and a delue for $. The want to earn at least $ per da. Write an inequalit that describes the goal. Graph the inequalit. Identif and interpret one combination that meets the goal., where represents basic washes and represents delue washes Number of delue car washes 6 Number of basic car washes (, ); basic washes and delue washes Online Quiz 6c. Less than or equal to ears; when is less than ears, will be greater than %. You cannot invest more than % of our mone. QUIZ 6. EXTENDED RESPONSE A financial advisor suggests that if a person is an aggressive investor, the percent of mone that the person invests in stocks should be greater than the difference of and the person s age. a. Graph Write and graph a linear inequalit that relates the percent of mone invested in stocks to an aggressive investor s age. > ; see margin for art. b. alculate If an aggressive investor is ears old, what are the possible percents that the investor can invest in stocks? Eplain our answer. c. Justif Are there an ages for which none of the solutions of the inequalit makes sense for this situation? Justif our answer. Solve the equation. See margin. 6. HALLENGE The formula m dv gives the mass m of an object in terms of the object s densit d and its volume V. Water has a densit of gram per cubic centimeter. An object immersed in water will sink if its densit is greater than the densit of water. An object will float in water if its densit is less than the densit of water. a. For an object that sinks, write and graph an inequalit that relates its mass (in grams) to its volume (in cubic centimeters). For an object that floats, write and graph an inequalit that relates its mass (in grams) to its volume (in cubic centimeters). See margin. b. A clindrical can has a radius of centimeters, a height of centimeters, and a mass of 9. grams. Will the can sink or float in water? Eplain our answer. Sink; the volume of the clindrical can is pr h p()() 8. cubic centimeters. Since the mass, 9. grams, is greater than the volume, 8. cubic centimeters, the can will sink..,. c 8, 6. r 6 8, Solve the inequalit. Graph our solution. 6. See margin for art.. > < or >. t < < t < 6. s s Graph the inequalit. or s 9. See margin.. 8. < 9. 8 Available at m.hrw.com Diagnosis/Remediation Practice A, B, in hapter Resource Book Stud Guide in hapter Resource Book Practice challenge Additional challenge is available in the hapter Resource Book. Quiz An easil-readable reduced cop of the quiz from the Assessment Book can be found at the beginning of this chapter. See. EXTRA PRATIE in Student Resources ONLINE QUIZ at m.hrw.com 6a, 6b, 6a, Quiz 9. See Additional Answers.