Chapter 3 ( ) ( ) Section 3.1. Chapter 3 Opener. Big Ideas Math Red Worked-Out Solutions. 3.1 Activity (pp ) Try It Yourself (p.

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1 Chapter Chapter Opener Try It Yourself (p. 9). y (). y () 9. y y () 9. q + 6. n 9. 6 p. h 9. t + 0. c Section.. Activity (pp. 0 ). a. Epression Value when 0 A. + + B. ( ) + C. + ( + ) D. + + E. ( ) + F. + + G. + ( ) H. ( + ) I. ( + ) J. ( + ) ( 0 + 0)

2 Chapter Epression Value when A. + + B. ( ) + C. + ( + ) D. + + () E. ( ) + F. + + G. + ( ) () () () () () H. ( + ) I. ( + ) J. ( + ) + () () () ( + ) + 0 Epression Value when 0 a. b c. 0 0 d. + 6 ( 0) e f g h i. + j Epression Value when a. b. + () c. () 0 d. + 6 () e. () f. + 0 () g. + + h. () i. + () j. + () + + A matches with d, B matches with e, C matches with j, D matches with i, E matches with g, F matches with a, G matches with h, H matches with f, I matches with b, J matches with c. b. Sample answer: The epressions in the right column have no parentheses and do not have more than one -term or more than one constant term. To obtain the equivalent epressions, the like terms are combined.

3 Chapter. Answer should include, but is not limited to: Students will write a lesson on simplifying an epression. They will describe the steps you can use to simplify an epression, write eamples using epressions from Activity, and write eercises using epressions different from the ones in Activity.. Sample answer: You can simplify an algebraic epression by: () using the Distributive Property to get rid of parentheses, () use the Commutative and Associative Properties of Addition to get the variable terms together and the terms without variables together, () combine the variable terms and combine the terms without variables.. 9. ( g + ) + g ( g) () + g g + g g + g + g g Sample answer: It may be easier to evaluate an algebraic epression for a given value when the epression is simplified. For real-life problems, it may be easier to recognize a value, like a total cost, based on the parts of a simplified algebraic epression.. On Your Own (pp. ). Terms: y,0, y Like terms: y and y. Terms: r, r, r, 9 Like terms: r and r. Terms:, p,, p, q. Like terms: and, p and p z + + z + z + z z + z + ( + ) z z z b b b b. ( q + ) ( q) + () q + q 0. Variable: The epression represents the amount of money the group spends at the movies. The total cost per person is $, which is $0. less per person.. Eercises (pp. ) Vocabulary and Concept Check. The terms of an epression are separated by addition. Rewrite the epression as y + ( ) + ( y) The terms are y,, and y.. Use the Distributive Property to add the coefficients of the like terms n and n. n + n + n n. no; The epression contains like terms, and, that should be combined. + ( + ). The algebraic epression + 6y is in simplest form because there are no like terms and no parentheses. Practice and Problem Solving. Terms: t,,t Like terms: t and t Each is each ticket $.0, large drink is and each is $.0, small $. popcorn The same number of each item is purchased. So, can represent the number of tickets, the number of large drinks, and the number of small popcorns. Epression:.0 + $ Terms: z,,, z Like terms: z and z, and

4 Chapter. Terms: n, n,, n Like terms: n, n, and n. Terms:, 9,, Like terms: 9 and 9. Terms:. y,,., y, z Like terms: and. 0. Terms: s,, s,, s Like terms: s and s, and. Like terms have the same variables raised to the same eponents. The term is not a like term because is squared. The like terms are and ( + 9) g g g g s s + 6 s + 6 s v 6.v.v 6.v (. 6.) v.v + a a a 9a ( 9) a. a. y + 9 y + + y 9 y y y 0 0 y 0 y. ( b ) ( b) b + 9 b p ( p + 6) p ( p) (6) p p 0 ( ) p 0 p 0 (c 9) + c ( c) ( 9) + c c c c + c + 6 ( + ) c + 6 6c + 6. Each weighs each weighs and each weighs sleeping. lb, backpack.6 lb, water. lb. bag bottle represents the number of hikers ( ) 0. The epression 0. indicates that the weight carried by each hiker is 0. pounds.. Before simplifying: + + () + () + () After simplifying: ( + ) () Sample answer: Simplifying the epression first is easier because you only have to substitute once instead of substituting three times.. + ( + y) + ( ) + ( y) + + y ( + ) + y + y + y + y + + y y ( + ) + ( ) y + y Because both epressions simplify to + y, they are equivalent.

5 Chapter. B; 6 ( ) 6 () ( ) Solution A: The epression inside the parentheses was simplified first, but and are not like terms. Solution C: The solution evaluated the epression from left to right by subtracting from 6, instead of using order of operations and distributing the first. Solution D: The solution did not distribute the negative sign to both of the terms inside the parentheses. A w ( ) ( ) () () The epression 9 + represents the area of the banner in square feet. 6. The earnings the earnings the earnings is is is for washing for waing for washing $, $, $0, each car each car each truck the earnings and for waing each truck is $. represents the number of cars. y represents the number of trucks y + y ( + ) + ( 0 + ) y 0 + y The epression 0 + y represents the earnings for washing and waing cars and y trucks.. Sample answer: ( + + ) ( + + ) ( + ) ( ) + ( ) +. Sample answer: ( + )( + ) ( )( ) 9. a. Area of Total Area of gold foil area red strips The total area is: A w ( 0) 0 square inches. Separately, the areas of the horizontal and vertical red strips are A w 0 square inches and A w square inches, respectively. Together, the two strips intersect. The intersection has an area of square inches. So, the area of the red strips is: Area + 0 ( + 0) square inches. Therefore, the area of the gold foil is: ( ) ( ) Area square inches. The epression 0 + represents the area of the gold foil in square inches. b. When, the area of the gold foil is square inches. () () c. Sample answer: England Fair Game Review 0.. in.,. in., in.,. in.,. in.. 0. m, 0. m, 0. m, 0.6 m, 0.6 m

6 Chapter. C; inches foot Elevation of bird s nest: ft Elevation of mole s den: ft ( ) The difference in height is feet. Section.. Activity (pp. 6 ). a. Sample answer: + b. Sample answer: c. Sample answer: + d. Sample answer:. a. Sample answer: ( + ) + ( + ) b. Sample answer: ( ) + ( ) + c. Sample answer: ( + ) + ( ) d. Sample answer: ( ) + ( + ). a. Sample answer: ( + ) ( + ) ( ) ( ) + + b. Sample answer: ( ) ( ) ( ) ( ) c. Sample answer: ( + ) ( ) d. Sample answer: ( ) ( + )

7 Chapter. a. Sample answer: ( + ) + ( ). Sample answer: Model the algebraic epressions using algebra tiles. To add: Combine like tiles and remove zero pairs. Write the resulting algebraic epression modeled by the remaining tiles. To subtract: Remove any like tiles from the first epression and the second epression. If tiles remain in the second epression, add the opposites of the tiles. Write the resulting algebraic epression modeled by the remaining tiles. ( + + b. Sample answer: ( 6) + ( + ) ) 6. Sample answer: ( + ) ( ) c. Sample answer: ( + ) ( + ) ) ( + + d. Sample answer: ( + ) ( ) ) + + (. On Your Own (pp. 9). ( + ) + ( ) ( z + ) + (z ) z + + z z + z +. ( n) + ( n + ) n 0n + 6 n 0n n + 0. ( w 6) + ( w + ) w + w + w + w + w + w + w. ( m ) ( m + ) m + m m + m m 6. ( c +.) (.c + ) c 6c 0 c 6c 0 c

8 Chapter. earnings selling price purchase price ( d + ) ( d ) ( d + ) + ( d + ) d + d + d d + + You earn $.. Eercises (pp. 90 9) Vocabulary and Concept Check. The algebraic epression is not linear because one variable has an eponent with a value not equal to.. The algebraic epression is linear because the variable has an eponent with a value of.. The algebraic epression is not linear because one variable has an eponent with a value not equal to.. Vertical method: Align like terms vertically and add or subtract; Horizontal method: Use properties of operations to group like terms and simplify.. The question "What is more than " is different. ( ) ( ) ( ) + ( ) + Practice and Problem Solving 6. Sample answer: ( 6) + ( + ). Sample answer: ( + ) ( ) ( ) ( ) +. ( n + ) + ( n ) n + + n n + n + n 9. ( b) + (b + ) b + b + b + b + + b (w 9) + ( w ) w 9 w w w 9 w. ( 6) + ( ) (.k ) + (k + ) k + k + k + k + k. ( q) + (.q + ) q + q + 6 q + q ( 0.9 h) + (.h ) 6.h.h.h.h + 6 h +. (9 6 m) + (m ) m + m m + m + m + 6. (z + ) + (z ) z + z z + z z

9 Chapter.. a. So, you have a total of w + in both accounts. So, you and your friend catch a total of m + 9 fireflies. b. Amount you catch: () + + Amount your friend catches: () Because > 6, you catch more fireflies. 9. ( g + ) ( g + ) g + g g g + g 0. (6d + ) ( d) 6d + + d 6d + d + 9d +. ( y) (.y ) y y + 6 y y y + 0. (n 9) (.n + ) n 9 + n 0 n + n 9 0 n 9. total amount in savings account ( c + 6) (6 + c) c + c c c + c + amount in checking account ( 0w + 0) + ( w + ) 0w w + 0w + w w + total amount you catch + amount your friend catches ( m + ) + ( m + 6) m + + m + 6 m + m m + 9. ( + 6) ( ) , not (m + 9) (m ) m + 9 6m + m 6m m + 6. a. From Eercise, you and your friend catch m + 9 fireflies after m minutes. Make a table that shows the number of fireflies caught after each minute. Time (minutes) + () () ( ) The number of fireflies caught increases by each minute. So, fireflies are caught each minute during the competition. b. At 0 minutes into the competition, you and your friend fireflies. already have caught Number of fireflies caught no; If the variable terms are opposites, the sum is a numerical epression.. Add the two given sides: (n + 6) + (n + ) n n + n + n n + Subtract the result from above from the perimeter: (n + ) (9n + ) n + 9n n 9n + n So, the epression that represents the measure of the third side is n. 9

10 Chapter 9. difference Cab Cruiser Charge tai Epress charge Let be the cost per mile. Cab Cruiser:. +.9 Tai Epress: (. +.9) (.6 +.6) Let be the width of the floor. Let + 0 be the length of the floor. ( ) + ( + 0) Because this epression counts the corner tiles twice, you must subtract from the epression to find the number of tiles. So, is the epression that represents the number of tiles along the outside of the room.. ( ) ( ) + + When : 0 0 When : y , or. D; Use a net to find the area of each face. Top: Bottom: Front: Back: Side: Side: ft side ft top back ft ft side ft front ft Fair Game Review.. + y y , or Surface Area So, the surface area is 0 square feet.. Etension (pp. 9 9) Practice.. Area of top The GCF is. bottom + Area of bottom 9 + () + () ( + ) The GCF is 6. 6() 6() 6( ) + Area of front + Area of back + Area of a side + Area of a side S

11 Chapter. The GCF is. + ( ) + () ( + ). y y The GCF is y ( y) () ( y ) 0z z The GCF is. 0z ( z) () (z ) w w 6 The GCF is. w + 6 ( w) + () (w + ) 6a a 6b b The GCF is. 6a + 6b (9 a) + ( b) (9a + b) m m 9n n The GCF is. m 9n ( m) ( n) (m n) 9. Factor out. b ( b ). Factor out Factor out. ( ) y + y. P s ( ) s ( ) s ( ) s ( ) s 6. a. So, the side length of the mat is ( ) feet. b. Table 6 ft ft ft A w Leaves ( + 6 ) 6( + ) 6( + ) ( + ) 6 + ft Etended Table ft ft Leaves So, the epression that represents the length of the etended table is (6 + ). The represents the shorter dimension of each leaf. ft 0. Factor out. d + + ( d ). Factor out ( + ). Factor out. h h 6

12 Chapter. A h ( b + b ) ( b + b) ( b + b) ( b + b) + ( b + b) + b + b + b + b ( ) ( ) Sample answer: One possible pair of epressions is and. A second possible pair is and. Study Help Available at BigIdeasMath.com. Quiz... Terms:, Like terms: and. Terms: 9, Like terms: 9 and. Terms:, 6,, Like terms: and, 6 and. Terms:,,, Like terms: and, and. ( + ) ( ) + ( ) 6 + ( 6 + ) ( + ) + 9. ( s + ) + (s ) s + + s s + s + s + 0. (9t + ) + (t 6) 9t + t + 6 t. ( k) + ( k + ) k k + 6 k k k +. ( q ) + ( q + 9) q + q + q + q + q + q q. ( n ) ( n + ) n + n n + n n 0. ( h ) ( 6h + ) h + + h 0 h + h + 0 9h +. Factor out. c ( c ) 6. Factor out. 9 j ( j ). Factor out...n n +. Factor out 6. 6z + 6( z ) Each costs each costs each costs and brush $.99, roller $6.9, paint can $.9. Let represent the number of brushes, the number of rollers, and the number of paint cans ( ).6 The epression.6 represents the total amount of money you spend for painting supplies. 6

13 Chapter 0. total apples apples you apples your friend + picked pick picks ( n ) ( n ) + + n + n + n + n + n + So, you and your friend pick ( n + ) apples. c. p The total number of apples you and your friend picked is one more than full baskets.. P + w ( w) + w 6w + w ( 6 + ) w w The epression w represents the perimeter of the eercise mat. So, p. d. t Section.. Activity (pp. 96 9). a. To get the variable tile by itself, remove the red tiles on the left side by adding three yellow tiles to each side. How many zero pairs can you remove from each side three So,. b. z 6 So, 0 t or t 0.. a. Remove the yellow tiles on the right side by adding two red tiles to each side. How many zero pairs can you remove from the right side two So, n. So, z. 6

14 Chapter b. y + 0. a. + So, y. c. + b So, or. b. So, b. d. + z So, 6. c. So,. So, z or z. 6

15 Chapter d.. w w.. The solution is w w So, or.. a So, F. b. Sample answer: The melting point of bromine is 9 degrees Fahrenheit. This is degrees Fahrenheit more than the melting point of mercury. So, subtract from 9 to get 9. So, the melting point of mercury is F. The method in part (a) is the algebraic solution because it assigns a variable to the unknown quantity. The method in part (b) is the arithmetic solution because it is a direct numerical solution that does not use any variables.. Sample answer: Use algebra tiles to model the equation. Then get the variable tile by itself by adding tiles and removing zero pairs. 6. Sample answer: To solve an addition equation, subtract to get the variable by itself. To solve a subtraction equation, add to get the variable by itself.. Sample answer: is a solution of one equation and is a solution to a different equation.. Sample answer: The value of a stock varies from day to day. The weights of golden retrievers vary from dog to dog.. On Your Own (pp. 9 99). p + + p The solution is p. p.. The solution is. The equation is 0.0 P.. s + + s Your friend s score is points.. Eercises (pp. 00 0) Vocabulary and Concept Check. To solve m + 6, use the Subtraction Property of Equality.. Addition and subtraction are inverse operations.. Check m in the first equation. m + + The profit today is $. less than the profit yesterday. Equation: 0.0 P. Your score is points less than your friend s score. Variable: Let s be your friend s score. Equation: s Because you get a false statement, the two equations are not equivalent. 6

16 Chapter. Solve the equations The equation + does not belong because it has a solution of 6, whereas the other three equations have the solution. Practice and Problem Solving. a 6 a a 9 The solution is a z + + z The solution is z.. k k The solution is k The solution is. 9. c c.6 The solution is c w w The solution is w.. z k c w q q 6 q The solution is q. 6 p p 6 p p The solution is p.. g g 0 The solution is g 0. g

17 Chapter. 9. d d The solution is d y... y.0 The solution is y d The solution is.. q q q The solution is q y r r 9 0 r r The solution is r 9. 0 w w w The solution is w. 6

18 Chapter 0. + k k + k The solution is k.. You need to use an inverse operation. Subtract from each side n + + n The solution is n.. c c The solution is c. + y + + y. y The solution is y.. p p The solution is p t t The outside temperature is.6 F.. P P The company s profit last year was $.6 million. h h + h h 0 The elevation of the helicopter is 9. Let be the unknown side length The difference in elevation of a helicopter and a submarine 0 meters. The unknown side length is centimeters. is meters. Variable: Let h be the elevation of the helicopter. Equation: The temperature of dry ice is h.9 F less than the outside temperature. Variable: Let t be the outside temperature. Equation: 09. t.9 A company s profit is $. million more than last year. Variable: Let P be the company s profit last year. Equation:. P +. 6

19 Chapter 0. Let be the unknown side length The unknown side length is. inches.. Let be the unknown side length The unknown side length is.9 feet. The height of the statue plus the height of the pedestal Variable: Let h be the height of the statue. is 0 feet.. Total distance 6 d d d The bus has traveled is distance already traveled kilometers. plus distance remaining. Variable: Let d be the distance the bus already traveled. Equation: 6 d + Equation: h + 0 h + 0 h The height of the statue is feet.. Your first jump 00 j j 0 0 j Your second jump is is 0 feet feet higher than your second jump. Variable: Let j be the height of your second jump. Equation: 00 j m m m 0.9 The missing angle measures Let p be your score in the fourth round. Because the leader has.6 points, you need a total score of.6 points to tie p.6. + p.6.. p 9.0 You need more than 9.0 points in the fourth round to win.. First solve + 6. Then substitute the result in the epression ( ) 9 So, the value of is 9.. The distance between 0 and on a number line is. The distance between 0 and on a number line is also. So, or. 69

20 Chapter The distance between 0 and 6 on a number line is 6. The distance between 0 and 6 on a number line is also 6. So, 6 or The distance between 0 and on a number line is. The distance between 0 and on a number line is also. So, or. Fair Game Review ( ) B; Students who voted for you 6 0 Female students who voted for you 0 9 So, 60 female students voted for you. Section.. Activity (pp. 0 0) a. Your goal is to get one variable tile by itself. Because there are variable tiles, divide the tiles into equal groups. 9 b. k So, k. c. t So, t or t. d. 0 m So, m or m. e. h 6 So,. So, h. 0

21 Chapter. a. d. So,. b. 6 So,. c. 0 So, 6.. a So, it takes. seconds. Divide the distance by the rate to get 00.. b c. So, the melting point of nitrogen is.6 F. Multiply the melting point of radon by.6 to get ( 6), or So, last year's profit is $ million. Multiply this year s profit by the reciprocal of to So, or. get 6. Sample answer: The method that uses the equation is the algebraic solution because it assigns a variable to the unknown quantity. The other method is the arithmetic solution because it is a direct numerical solution that does not use any variables.

22 Chapter. If you have an equation involving multiplication, you divide each side by the same (nonzero) number. If you have an equation involving division, you multiply each side by the same number. Sample answer: 9 9. On Your Own (pp. 0 0). ( ) 0 The solution is 0.. a a a The solution is a...n.n.. n The solution is n. 0 a.n.. ( ) ( ). The solution is. b b b b The solution is b. 6.. h 9 h h ( 9) The solution is h. 0.t 0.t t h 9 ( ) The record low temperature in Alaska is 0 F.. Eercises (pp. 06 0) Vocabulary and Concept Check. You can use multiplication to solve equations involving division because multiplication and division are inverse operations.. Sample answer: Opening a door and then closing the door are inverse operations. Walking from home to the store and walking from the store back home are inverse operations.. Dividing by will undo multiplying by.. Adding will undo subtracting.. Multiplying by will undo dividing by. 6. Subtracting 6 will undo adding 6. Practice and Problem Solving. h h h h The solution is h.. t t t 9 The record low in Hawaii The solution is t 9. is 0. times the record low in Alaska. Variable: Let t be the record low in Alaska. Equation: 0. t t 9

23 Chapter 9. n n n n n..6 n n n.6.6 The solution is n. The solution is n. k 0. 9 k 9 k The solution is k.. m 0 m 0 m The solution is m.. t t t The solution is t The solution is. k m 0 ( ) t ( ) b b 0 0 b 0 ( 0) 0 0 b 0 0 The solution is b 0.. 6p 6p 6 6 p The solution is p. 6p p. 0.6 p p The solution is p. g g g 6 The solution is g p g ( ) 6 c c c 0 0 c The solution is c 0. f f 9 f 6 f 9 9 The solution is f d d 9 d The solution is d 9. d 9

24 Chapter. 6 y 6 y 6 y 6 y 6 y The solution is y 6.. You need to divide each side by Let be the number. An equation is The solution is.. Let be the number. An equation is 0 0 The solution is Let be the number. An equation is. The solution is.. Let be the number. An equation is The solution is.. 0.n 6 0.n n You have to sell newspapers to buy the eercise cleats. 9. Amount earned The rock climber climbs feet in 0 minutes. 0. Sample answer: a b..... times number of newspapers Variable: Let n be the number of newspapers. is the cost of the cleats. Equation: 0. n 6 Rate equals distance divided by time. Variable: Let be the distance. Equation: 0

25 Chapter. Sample answer: a.... b Sample answer: a. b Sample answer: a. b.. To solve c 6, you can divide each side by or multiply each side by or multiply each side by, then divide each side by Stock return.6n 0.0.6n n After days, the total return is $0.0. Equation: s 6 s 6 s 9 There are 9 students. 6 0 So, 0 feet. ( 6) 0.60 b b 6 0. b times number of days Variable: Let n be the number of days. So, you save $0. $0.60 $0. by buying the bike at Store A. is the total return. Equation:.6 n 0.0 Portion of times the equals the students that voted number of students number of ballots. Variable: Let s be the number of students. s 6 The price of a bike at Store A is the price at Store B. 6 Variable: Let b be the price at Store B. Equation: 0.60 b 6

26 Chapter 9. m 0 m 0 m The distance between 0 and on a number line is. The distance between 0 and on a number line is also. So, m or m. 0. Distance already traveled miles Find the rate of travel after days using the formula for distance. d rt 6 9 r 60 r 60 r r r Your rate of travel is miles per day. 6 You have 0 9 miles left to travel. Find the time using the formula for distance. d rt t 00 t 00 t t t Fair Game Review. + ( ). + ( ) 9. ( ) +. ( ) B; of the apartments have not been scheduled to receive new carpet. Section.. Activity (pp. 0 09). Remove the three red tiles on the left side by adding three yellow tiles to each side. How many zero pairs can you remove from each side three Because there are two green tiles, divide the red tiles into two equal groups. So,. You have more days until you reach your destination. 6

27 Chapter. Write the equation. b. + + Add to each side. Simplify. Divide each side by. Simplify. So,. a. The first step is adding to each side. b. You use the same steps to complete the problem in Activity as you do in Activity, only you do not use algebra tiles.. a. + 6 So, So, or b. Your account now has a balance of $0.6. You withdrew $. for groceries, so add $. to $0.6. You tripled your balance by making a deposit, so find of $ You had $.9 in your account before the deposit.. Sample answer: Model the equation using algebra tiles. Remove the smaller tiles by adding positive tiles to both sides if the original tiles are negative or adding negative tiles to both sides if the original tiles are positive and then removing all pairs of positive and negative tiles. If there are multiple larger tiles, divide the smaller tiles into equal groups and circle them. Keep one of the groups. This shows the value of.

28 Chapter 6. The first step is to subtract from both sides of the equation z. + 9 z + 9 z z z z The steps are the same. The solution is z.. On Your Own (pp. 0 ). + + The solution is.. c c c c c The solution is c ( ) The solution is. m m m m m The solution is m c ( ) () m a 6 + a a a a 6 + a 6 + The solution is a y + 9 y 9 y 9 y 6 y 6 y The solution is y.. 0 The solution is. y + 9 () ( ) ( ) 0 + 0

29 Chapter 9..m.m 0.m 0.m m The solution is m h 00 0h h 9 0h h 9. The height is 9. feet.. Eercises (pp. ).m.m Vocabulary and Concept Check. To solve two-step equations, you undo the operations in the reverse order of the order of operations.. B; The first step in solving + n is to subtract.. D; The first step in solving n is to divide by. n. C; The first step in solving is to multiply by. n. A; The first step in solving is to add. Practice and Problem Solving 6. v + v + v + ( ) + v v + v The solution is v.. b + 9 b + 9 b b b The solution is b. b k + k + 9 k 9 k 9 k k The solution is k. k t 6t 6t + + 6( ) 6t 6t 6 6 t The solution is t. 0. n n n.6 n.6 n. n The solution is n... g +.. g g. g. g. g The solution is g.. 9

30 Chapter. t 0 t t t t t The solution is t.. p + 9 p p p p p The solution is + 9 p The solution is.. +.h. +.h..h..h... h. +.h The solution is h f f f.. f... f.. f The solution is f....y..9.y y 6..y 6... y 6..y The solution is y 6... The first step should be to add 6 to each side

31 Chapter 9. In the second step, you should divide each side by, not g 0 g g g g ( ) g 0 g 0 ( ) The solution is g.. a 6 a a 6 a a a a The solution is a.

32 Chapter.. + z z z 6 z z z The solution is + z The solution is b. z b b b 9 b 9 b b The solution is v + 9 v v 0 9 v v 0 9 v The solution is v

33 Chapter 6. equals. Equation: It will take 9 hours.. Cost to rent bowling shoes You can bowl three games. plus cost per game times Variable: Let be the number of games. number of games Equation:.0 +. Temp. at :00 P.M. plus temp. change per hour Variable: Let be the number of hours. equals total amount you have. Equation: 9. times number of hours Equation: + ( ) You had tet messages. 9. v 9v 0 6v 0 6v v The solution is v. 0. t t t t t The solution is t.. d d + d 6d 6d 6 6 d Monthly fee plus cost per tet message equals amount you owe. Equation: 9.0 times Variable: Let be the number of tet messages. v 9v 0 ( ) ( ) t t d d + d number of tet messages Equation: The solution is d

34 Chapter. ( ) The solution is.. ( m ) + m m m + + m 6 m 6 m 9 The solution is m y 9 0 y 0 y y y y. ( y ) ( y + 9) 0 ( + 9) The solution is y. ( ) ( ) 6 6 ( m ) Sample answer: You travel halfway up a ladder. Then you climb down two feet and are feet above the ground. How long is the ladder The ladder is 0 feet long. 6. l + w P ( m) + m 0 6m + m 0 m 0 m 0 m So, m.. You need to know the initial fee.. You need to know the coldest surface temperature on the moon. 9. a. Each group has nine insects. 9 The insects are divided into groups, 9 so multiply by. Five insects escape, so add. + So, you caught insects. b So, you caught insects, which is the same answer obtained in part (a). The diver s elevation d + d + d ( ) d d The elevation of the entrance is feet. is foot deeper than of the elevation of the entrance. Variable: Let d be the elevation of the entrance. Equation: d

35 Chapter. Let be the amount by which you should change the length. P + w ( + ) You should decrease the length of the rectangle by 0 centimeters. Fair Game Review So, So,.6 ( ) C; ( ) Quiz The solution is.. + p 9 p,or 0 + p The solution is p 0. b. b b The solution is b.. w w. w. w. w The solution is w.. b

36 Chapter. b b The solution is b 0.6. a a, or 0 0 The solution is. 0 0,or 96 The solution is. k.6 k k. k. k.6 The solution is k So, ,or. So, You had $9. in your bank account before you withdrew the money.. Current balance equals original balance Variable: Let b be the original balance. The water times number level change of days per day ( 6) minus amount withdrawn. Equation: equals 6 feet. Variable: Let be the number of days. Equation: 6 It takes days for the water level to change 6 feet So,.. 6

37 Chapter. Time played per quarter times number of quarters plus time you did not play Variable: Let be the average time played per quarter. Equation: + b. Mat length minus picture length divided by Variable: Let be the amount to be cut. equals Equation: ( 9.6 6) the sum of the amount cut and 0.. Equation: + 0. equals length of game. Equation: + 6 9,or6 Your mean playing time was 6 minutes per quarter You should cut. inches from the top and bottom. Chapter Review. Terms: z,, z Like terms: z and z. Terms:,, n n, Like terms: n and n, and. Terms: 0, y,, Like terms: 0 and. h h h. a. Mat width minus picture width divided by equals Variable: Let be the amount to be cut. Equation: (. ) the sum of amount cut and 0.. Equation: + 0. You should cut. inches from the left and right sides.. 6.r.9r 6.r.9r.r ( + q) q + q q +. (6m ) 6 m m m 9..( n) n +..n 6 +..n.

38 Chapter 0. ( c ) + (c + 9) c + c + 9 c + c + 9 c +. 0 ( d 0) ( d + 6) d d 0 d d d d d. Factor out. b + ( b + ). Factor out. y + y +. Factor out.. ( j ). j... Factor out. ( p ) p p + + p The solution is p q 6 6 q The solution is q.. + j + + j 0 The solution is j b b The solution is b. p 6 + q j + 0 b n + n The solution is n. n v v v The solution is v. t t.9. The solution is t The solution is 9.. The solution is. t

39 Chapter y. y 9 y 6.. The solution is y 9. y y 9 z z z z The solution is z. w. 0 w w 0 The solution is w 0.. The solution is y 0 y y The solution is y. 0..z..z... z 6 The solution is z w. 6.w w 0. The solution is w 0.. w ( ) 0 y z w Equation: c. c. c (.) c 6 The total change over the five-day period is 6 F.. c + 6 c c c c The solution is c. 0 w 0 9w 0 9w w 9w 9 9 w 9. ( w ) ( w ) The solution is Total change divided by w. 9 number of days Variable: Let c be the total change. equals mean temperature change. c

40 Chapter. w + 6 w + 6 w 6 w 6 6 ( ) 6 w w The solution is w The solution is.... n +..n..n n 6..n 6... n It will take years for the canyon floor to have an elevation of feet. Chapter Test.. Elevation change per year + + ( + ) 0 times number of years Variable: Let n be number of years. Equation:..w y + w.w + w y (. + ) w y 6.w y n + 9n n + 9n 6n + 9n + ( 6 + 9) n + n. plus current elevation n + (.) equals feet. Equation: j + + j j + + j. j + j + j + 90

41 Chapter p + + 6p 6p p 6p + 6p + 9 p r 6r + r + 6r r + 6r r...( s ) (.s.) s +..s +.6 s.s s Factor out. n ( n ) 0. Factor out. q + +. The solution is. ( ). ( q ) The solution is. g g 9 g 6 ( ) The solution is g 6. ( ) ( ) + + g 9 ( ) 6 9. z z 9. The solution is z 9.. z c 6c 6c c,orc The solution is c k 9 k + + k k ( ) k 9 k 9 ( ) The solution is k.. Each costs each costs each costs women s $, women s $, men s $, haircut shampoo haircut and each costs men s $. shampoo w represents the number of women. m represents the number of men. w + w + m + m + w + + m w + m The epression w + m represents the income from w women and m men getting a haircut and a shampoo. 9

42 Chapter. To match the world record, the total time difference is 0. Let be the time difference for lap The runner needs a time difference of 0.6 for the fourth lap Your score before the penalty is ,or So,. Chapter Standards Assessment b. B; Final score cd d ; G; +. is score before penalty minus penalty. Variable: Let be your score before the penalty. Equation: B; Mean The mean temperature of last week is 6 F.. F; So, 0. ( 0.0).. D; 96 6( ) F; P l + w 00 ( j) + (60) 00 j j j 0 j j B; + y H; , or 6 9

43 Chapter. Part A: The total the amount the amount equals plus cost of the you have you plan to bicycle saved save times the number of weeks. Variable: Let w be the number of weeks. Equation: w w w w..w..w.. 0 w So, it will take 0 weeks. Part B: The total minus coupon equals the amount cost of the you have saved bicycle plus the amount times the number you plan of weeks. to save Variable: Let w be the number of weeks. Equation: w w w w w.0.w.0.w.. 6 w weeks sooner because in Part A it takes 0 weeks and in Part B it takes 6 weeks. The difference is 0 6 weeks. 9

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