Simplify each expression. 1. 2n - 3n n. Evaluate each expression a + 4a for a = 5 43 EXAMPLE

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1 -. Pln - Solving Multi-Step Equtions Objectives To use the Distributive Property when cobining like ters To use the Distributive Property when solving equtions Eples Cobining Like Ters Rel-World Proble Solving Solving n Eqution With Grouping Sybols Solving n Eqution Tht Contins Frctions Solving n Eqution Tht Contins Decils Mth Bckground You y need to illustrte Eple in greter detil by writing c c ( )c. Students often lose sight of this use of the Distributive Property. More Mth Bckground: p. C Lesson Plnning nd Resources See p. E for list of the resources tht support this lesson. Bell Ringer Prctice Check Skills You ll Need For intervention, direct students to: Eponents nd Order of Opertions Lesson -: Eple Etr Skills nd Word Proble Prctice, Ch. The Distributive Property Lesson -: Eples, Etr Skills nd Word Proble Prctice, Ch. Wht You ll Lern To use the Distributive Property when cobining like ters To use the Distributive Property when solving equtions... And Why To solve proble involving building fence, s in Eple Prt Cobining Using the Distributive Like Ters Property to Cobine Like Ters Proble Solving Hint You use the Distributive Property whenever you dd or subtrct like ters. ± ± ( ± ) Chpter Solving Equtions Check Skills You ll Need GO for Help You cn solve equtions tht require ore thn two steps. If there re like ters on one side of n eqution, first use the Distributive Property to cobine the. Then use the properties of equlity to solve the eqution.. c c 78 c c 78 c 78 c b. b b b b b b Cobining Like Ters Cobine like ters. Subtrct fro ech side. c Siplify. c Divide ech side by. c Siplify. b b - - Use the Couttive Property of Addition. Cobine like ters. Subtrct fro ech side. b 0 Siplify. b 0 Divide ech side by. b Siplify. Lessons - nd - Siplify ech epression.. n - n n. - b b 8b. 9(w - ) 9w. -0(b - ) 0b ± 0. (- ) ±. ( - w) 0 w Evlute ech epression for for - 9. (8n ) for n (7 y) for y Check your nswer b. 7 - c. -y y d. -z 8 (z) - Specil Needs L Use counters to reind students how the Distributive Property cn siplify solving equtions. For eple, in Eple, use red counters nd red counter for (c c) in the eqution. Cobine the counters to ke c( ). lerning style: tctile Below Level L Reind students to ultiply ll ters within prentheses by the nuber before the prentheses. Also wrn the to py ttention to the signs of the nubers. lerning style: verbl

2 Rel-World Connection In the United Sttes, there re pproitely 0,000 cities with counity grdens. You cn odel rel-world situtions using ulti-step equtions. Rel-World Proble Solving Multiple Choice A grdener is plnning rectngulr grden re in counity grden. His grden will be net to n eisting -ft fence.the grdener hs totl of ft of fencing to build the other three sides of his grden. How long will the grden be if the width is ft? ft ft ft ft length length Relte plus ft plus equls of side of side Define Let length of side djcent to the fence. Write - - Cobine like ters on the left side of the eqution. Subtrct fro ech side. Siplify. Divide ech side by. Siplify. The grden will be ft long. So D is the correct nswer. ount of fencing A crpenter is building rectngulr fence for plyground. One side of the plyground is the wll of building 70 ft wide. He plns to use 0 ft of fencing teril. Wht is the length of the plyground if the width is 70 ft? ft ft. Tech Guided Instruction Tctile Lerners Let students odel nd solve the eqution with tiles to help the understnd tht c c c. Additionl Eples Solve 90. You need to build rectngulr pen in your bck yrd for your dog. One side of the pen will be ginst the house. Two sides of the pen hve length of ft nd the width will be ft. Wht is the gretest length the pen cn be if you hve ft of fencing? 9 ft Auditory Lerners Hve pirs of students tke turns eplining the steps of this eple to ech other. Then, hve the work together to solve the Check Understnding eercises. Using the Distributive Property to Solve Equtions In the eqution -(b - ), the prentheses indicte ultipliction. Use the Distributive Property to ultiply ech ter within the prentheses by -. Then use the properties of equlity to solve the eqution. Additionl Eples Solve ( - ) 8. 7 A B C D E A B C D E A B C D E A B C D E A B C D E B C D E Test-Tking Tip Reeber to ultiply the nuber outside the prentheses by both ters inside the prentheses. Solving n Eqution With Grouping Sybols Solve -(b - ). -b 8 Use the Distributive Property. -b Subtrct 8 fro ech side. -b Siplify. b Divide ech side by. b - Siplify.. (k 8) b. -( - ) 9 Lesson - Solving Multi-Step Equtions 7 Advnced Lerners L Chllenge students to solve the eqution in Eple by different ethod thn the one shown. lerning style: verbl English Lnguge Lerners ELL Soe students y not know wht counity grden (referred to in Eple ) is. Let student who hs seen or prticipted in counity grden eplin wht one is nd how it is run. lerning style: verbl 7

3 Additionl Eples Solve 7. 0 Solve Mth Tip Review with students tht they cn use ny coon denointor to solve n eqution. To deonstrte, tell students to solve the eqution using coon denointor of. Mth Tip Reind students tht decils represent frctions tht hve powers of 0 s denointors. The nuber of decil plces is the se s the nuber of zeros in the power of 0. Resources Dily Notetking Guide - L Dily Notetking Guide - Adpted Instruction L Closure Ask: How cn you cler n eqution of frctions or decils? If n eqution involves frctions, ultiply ech side of the eqution by coon ultiple of the denointors. If n eqution involves decils, ultiply ech side of the eqution by power of 0. The power equls the gretest nuber of digits to the right of ny decil point. Vocbulry Tip nd both represent. nd both represent. Proble Solving Hint Powers of 0: ,000 Following re two wys you cn solve n eqution like 7. Solving n Eqution Tht Contins Frctions Solve 7. Method Adding frctions 7 7 Rewrite the eqution with frctions s coefficients. 7 Write the frctions with denointor of. 7 7 Cobine like ters. 7 Q 7 7 R 7(7) Multiply ech side by 7, the reciprocl of. Siplify. Method Multiplying to cler frctions 7 Multiply ech side by, Q R (7) coon ultiple of nd. Q R Q R (7) Use the Distributive Property. Multiply. 7 Cobine like ters Divide ech side by 7. Siplify. Eplin why you chose the ethod you used.. b b. Eplntions y vry. You cn cler n eqution of decils by ultiplying by power of 0. In the eqution , the gretest nuber of digits to the right of decil point is. To cler the eqution of decils, ultiply ech side of the eqution by 0, or 00. Solving n Eqution Tht Contins Decils Solve (0. 8.7) 00(.) Multiply ech side by 0, or (0.) 00(8.7) 00(.) Use the Distributive Property. Siplify. Subtrct 87 fro ech side. 0 0 Siplify Divide ech side by 0. 9 Siplify b Chpter Solving Equtions 8

4 Keep the steps in the sury below in ind s you solve equtions tht hve vribles on one side of the eqution. Key Concepts Sury Steps for Solving Multi-Step Eqution Step Step Step Step Step Cler the eqution of frctions nd decils. Use the Distributive Property to reove prentheses on ech side. Cobine like ters on ech side. Undo ddition or subtrction. Undo ultipliction or division.. Prctice Assignent Guide A B -,, -, 9- A B -,, 7-8, - C Chllenge -8 Test Prep 9-7 Mied Review 7-9 EXERCISES Prctice nd Proble Solving For ore eercises, see Etr Skill nd Word Proble Prctice. Hoework To check students understnding of key skills nd concepts, go over Eercises 0,,,, 8. A GO Prctice by Eple for Help Eple (pge ) Eple (pge 7) Check your nswer.. n - n 8 9. y y c n n b - b - 0 Write n eqution to odel ech sitution. Solve your eqution. 0. Two friends re renting n prtent. They py the lndlord the first onth s rent. The lndlord lso requires the to py n dditionl hlf of onth s rent for security deposit. The totl ount they py the lndlord before oving in is $7. Wht is the onthly rent? ± 7; $0. You re fencing rectngulr puppy kennel with ft of fence. The side of the kennel ginst your house does not need fence. This side is 9 ft long. Find the diensions of the kennel. ± 9 ± ; 8 ft by 9 ft GPS Guided Proble Solving L Enrichent Reteching Adpted Prctice L L L Prctice Ne Clss Dte Prctice - Solving Inequlities Using Addition nd Subtrction Solve ech inequlity. Grph nd check the solution.. n y.. r.7. 7 b. n. 7 $ c 7 7. g d f d v 9. - t 9. y d 9 8. s 9. 9 h t -. L Eple (pge 7) Check your nswer.. (8 p). ( - ) 8. -(q - ) Write nd solve n inequlity tht odels ech sitution.. It will tke t lest 0 points for Kiko s te to win the th contest. The scores for Kiko s tetes were 9, 8, nd 87, but one of Kiko s tetes lost of those points for n incoplete nswer. How ny points ust Kiko ern for her te to win the contest?. This seson, Nor hs t-bts in softbll. By the end of the seson she wnts to hve t lest 0 t-bts. How ny ore t-bts does Nor need to rech her gol?. ( - ). ( - ) ( ) -0. The verge wind speed incresed 9 i/h fro 8 A.M. to noon. The verge wind speed decresed i/h fro noon to P.M. At P.M., the verge wind speed ws t lest i/h. Wht is the iniu vlue of the verge wind speed t 8 A.M.? Eple (pge 8) ( ) 9. (y - ) 9 0. ( y) k y w Person Eduction, Inc. All rights reserved.. Suppose it tkes no ore thn in for you to get to school. If you hve trveled for. in lredy, how uch longer, t ost, ight you tke to get to school?. Jon hs strted physicl fitness progr. One of her gols is to be ble to run t lest i without stopping. She cn now run. i without stopping. How ny ore iles ust she run non-stop to chieve her gol?. Suppose you cn get higher interest rte on your svings if you intin blnce of t lest $000 in your svings ccount. The blnce in your svings ccount is now $08. You deposit $.0 into your ccount. Wht is the gretest ount tht you cn withdrw nd still get the higher interest rte? Solve ech inequlity. Grph nd check the solution. z d 0 9. v f w -. b. t u z 7. 8 b 8. k b 7. 8 k -. j..8 Eple (pge 8) y.8.. s - s 0...0y p y y Lesson - Solving Multi-Step Equtions 9 9

5 Error Prevention! Eercise Be sure students don t confuse the enings of epty with full. Hve student volunteer drw two cups on the bord. Hve the student shde the cups so tht one ppers epty nd the other full. Lbel ech cup. B Apply Your Skills. Answers y vry. Sple: Cobine nd first to siplify the left side of the eqution t - t (z ) ( - ) 0. 8y - (y - ) 9. y.. ( ) (.c ) p 0.(0 - p).08. Error Anlysis Eplin the error in the student s work t the right. The student forgot to ultiply by Criticl Thinking Suppose you wnt to solve the eqution - -. Wht would you do s your first step? See left.. Writing To solve ( - ) 7, you cn use the Distributive Property, or you cn ultiply ech side of the eqution by -. Which ethod do you prefer? Eplin why. Answers y vry. Sple: Multiply by to eliinte frctions. Geoetry The perieter of ech rectngle is in. Find the vlue of.. in.. ( ) in. in. CANOE RENTAL $.00 per hour $.00 life jcket Use n eqution to solve ech proble.. John nd two friends rent cnoe t prk. Ech person ust rent life jcket. If the bill for the rentl of the cnoe nd life jckets is $, for how ny hours did they rent the cnoe? 7 h 7. Moving Costs The McNeills rented oving truck for $9.9 plus $.0 per ile. Before returning the truck, they filled the tnk with gsoline, which cost $8.. The totl cost ws $9.87. Find the nuber of iles the truck ws driven. 9 i 8. Cell Phones Jne s cell phone pln is $0 per onth plus $. per inute for GPS ech inute over 00 inutes of cll tie. If Jne s cell phone bill is $8.00, for how ny etr clling inutes ws she billed? 0 in 9. Open-Ended Write n epression with four ters tht cn be siplified to n epression with two ters. Answers y vry. Sple: ± ± 9 Geoetry Find the vlue of.(hint: The su of the esures of the ngles of tringle is 808.) ( ) 0 ( ) 0 Chpter Solving Equtions 0

6 GO nline Hoework Help Visit: PHSchool.co Web Code: te-00. Purchsing The function c p 0.07p reltes the price of n ite p with its cost c fter 7% t is dded. A student hs $.0. Wht is the cost of the ost epensive ite he cn buy? $.8. Finnce Ndi hs $70 in her bnk ccount. Ech week she deposits $ fro her llownce nd $ fro bbysitting. The function b 70 ( )w reltes her bnk blnce b to weeks w. When will she hve $0 in her bnk ccount? weeks. Tyr solves n eqution using her grphing clcultor. Use the screens below. Plot Plot Plot Y (X ) Y Y Y Y Y Y7 Intersection X Y. Assess & Retech Lesson Quiz ( - ) 7. n n Alterntive Assessent C Chllenge. Wht ws the originl eqution tht Tyr ws solving? ( ) b. Wht is the point of intersection? (, ) c. Show tht the -vlue of the intersection solves the originl eqution. ( ) () For Eercises 8, use n eqution to solve ech proble.. Crs You fill your cr s gs tnk when it is bout epty. The net week, you fill the tnk second tie when it is bout epty. If you buy totl of 8 gl of gs on these two dys, bout how ny gllons does the tnk hold? bout gl 7. A work crew hs two pups, one new nd one old. The new pup cn fill tnk in hours. The old pup cn fill the se tnk in 7 hours.. How uch of tnk cn be filled in hour with the new pup? With the old pup? ; 7 b. Write n epression for the nuber of tnks the new pup cn fill in t hours. (Hint: Write the rte t which the new pup fills tnks s frction nd then ultiply by t.) t c. Write n epression for the nuber of tnks the old pup cn fill in t hours. 7 t d. Write nd solve n eqution for the tie it will tke the pups to fill one tnk if the pups re used together. t ± 7 t ; h 8. Investing Mr. Firbnks invested hlf his oney in lnd, tenth in stock, nd twentieth in bonds. He put the reining $,000 in svings ccount. Wht is the totl ount of oney tht Mr. Firbnks sved or invested? $00,000 Write 0.( - ) Hve students solve the eqution showing ll work. Instruct the to write the nuber of the Step fro p. 9 tht is used for ech step of the solution. Test Prep Resources For dditionl prctice with vriety of test ite forts: Stndrdized Test Prep, p. 9 Test-Tking Strtegies, p. 90 Test-Tking Strtegies with Trnsprencies Test Prep Multiple Choice 9. Wht is the vlue of the epression -r r when r -? C A. - B. - C. 0 D. 70. Solve 8n - n. H F. G. H. J If nuber is incresed by nd tht nuber is doubled, the result is -8. Wht ws the originl nuber? A A. -7 B. -. C. D. lesson quiz, PHSchool.co, Web Code: t-00 Lesson - Solving Multi-Step Equtions

7 7. The gs tnk in Royston s cr holds gl of gsoline. The cr verges 9 i/gl. Royston filled up the tnk nd then drove 0 i. About how ny gllons of gsoline re left in the tnk? G F. gl G. 7 gl H. 8 gl J. 9 gl 7. Josie s gol is to run 0 iles ech week. This week she hs lredy run distnces of. iles,. iles, nd. iles. If she wnts to spred out the reining iles evenly over the net dys, which eqution cn you use to find how ny iles () per dy she ust run? C A B C D A cell phone copny chrges $. for the first inute but only $.0 every inute fter tht. Which eqution cn you use to find how ny inutes Eric tlked if the bill for the cll ws $.? F F ( - ). G H ( - ). J Mied Review GO for Help Lesson - Lesson - Lessons - through - 7. y n c y p 0 7 Mentl Mth Siplify ech epression. 8.?? ?? ? 8? Siplify ech epression ? (-) (-) 9. (-) (-) (-) 9. -? (-) Algebr t Work Airline Pilot Airline pilots ke ny clcultions before, during, nd fter flight. Pilots study wether conditions to deterine the sfest ltitude, route, nd speed for flight. Pilots clculte lift, which ust equl the irplne s weight in pounds. An irplne s lift cpbilities re clculted using the forul L dv s, where L is the lift, d is the density of the ir, v is the velocity of the ircrft in feet per second, s is the wing re of the ircrft in squre feet, nd is vlue deterined by the type of irfoil the irplne hs nd the pitch ngle of the irplne. PHSchool.co For: Infortion bout creer s n irline pilot Web Code: tb-0 Chpter Solving Equtions