3.1 Algebraic Expressions. Parts of an algebraic expression are called terms. One way to simplify an expression is to combine like terms. 4x 2.

Transcription

1 3.1 Algebraic Expressions Parts of an algebraic expression are called terms. One way to simplify an expression is to combine like terms. What does it mean to combine like terms? 4x 2 You can only combine like terms that have the same: and Circle the like terms for each line: 4x 9 2x 2 7x 5x 10x 5x 2 10x 2 7y y 2y 18y 14m 3n 2 2n 2 3m 2 When simplifying an expression: 1. Distribute 2. Combine like terms 3. Remember: Keep the sign with the number that comes after it.

2 7U3L1 Name ID: 1 l a2r0[1m5` kknumtzac isbosfutvwhaurgem WLIL[Cq.Q d XA_laly PrpiXg\hDtXsl ErZeesBemrxvFegdX. Algebraic Expressions Simplify each expression. 1) - 8 p - p 2) 13k k Date 3) x x 4) 1-4 x x 5) - 12r - 3r 6) 2b - 13b 7) - 14 x - 11 x 8) - 9m - 5m 9) - 7b - 10b 10) 9-14 x - 4 x _ n2o0n1_5x dkgubthai hsxo]fctpwvazrreq LLdL[CA.` e QAAlslH UrSingihxt]sh nrpegsteurnv[eqdc.q K FMWaFdVer Qwzi\tMhY VIXnXfciHnriYtdeD EPPrteZ-eAiligBekbtrHac. -1- Worksheet by Kuta Software LLC

3 11) 9(5 + 2v) - 3v 12) 2(8 + 11r) + 2r 13) 4-14(4-11a) 14) 3(n + 7) ) - 14n + 8(1 + 5n) 16) - 12( a) - 5a 17) - 8(- 13m - 9) - 10m 18) 14(n - 1) ) (1 + 9b) 20) 14(1 + 5 x) + 3 v `2F0A1I5m bkpuwtdav rsiovfctuwtaarhea hlpllcy.a A qaelblk nr[idgshpttsd qrwe^spekrhvgebdm.f y MMaaGdven Cwvi]tmhU lion_fqicnqidtjed pper[eq-sa\lvg\egb`rhad. -2- Worksheet by Kuta Software LLC

4 Name Date 3.1 Practice For use after Lesson 3.1 Identify the terms and like terms in the expression x 4 7x y 0.7 y 1 6.4y Simplify the expression. 3. 5a 2a 9 4. m 1 5 4m w w 7 d g 2 4k g p p 9. Write an expression in simplest form that represents the cost for shampooing and cutting w women s hair and m men s hair. Women Men Cut $15 $7 Shampoo $5 $2 46 Big Ideas Math Red Accelerated Copyright Big Ideas Learning, LLC Record and Practice Journal

5 Name Date 3.2 Practice For use after Lesson 3.2 Find the sum or difference. 1. x 2 x n 4 4n y 1 2y k k g g 6. 2r r 7. You earn 4x 12 then lose 2x 5 number of points you have now. points after completing x levels of a video game and points. Write an expression that represents the total 50 Big Ideas Math Red Accelerated Copyright Big Ideas Learning, LLC Record and Practice Journal

6 Name Date 3.2 Practice A Find the sum. 1. p 3 p n 1 4 n 3. 3r 8 5r x 3 2x c c q 2 7.5q y y 8. 6x x 9. After a week of rain, tadpoles appeared in your pond. After t minutes, you have (7t + 5) tadpoles and your friend has (8t 3) tadpoles. a. Write an expression that represents the number of tadpoles you and your friend caught together. b. Who has more tadpoles after 9 minutes? Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 73

7 Find the difference. 10. k 3 3k d 2 7 2d j 7 9 j x x t 5 1.6t w 8 10w The admission to a local fair is $10 for each adult and $6 for each child. Each rides costs $1.50 for an adult and $1 for a child. a. Write an expression that represents how much more an adult will spend at the fair. b. An adult and a child each go on 7 rides. How much more did the adult spend? 17. Write an expression that represents the perimeter of the triangle. 74 Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

8 Name Date 3.2 Practice B Find the sum t 3t k 9 4k y 6 2y g g s s 6. 6p 3 7 p w w 8. 16k k 9. You are selling tickets to a play. You have sold 3t 2 and 2t 5 tickets for $7 each. tickets for $5 each a. Write an expression that represents the total number of tickets sold so far. b. Write an expression that represents the total amount of money received for the tickets that have been sold. c. When t 3, what is the total amount of money received? Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 73

9 Find the difference u 5u x 7 6 5x h h b 3 0.9b j j n 6 10n 2 16.You are collecting pairs of socks and toothbrushes for a local charity. After d days, you have collected 4d 5 pairs of socks and 3d 7 toothbrushes. a. Write an expression that represents the total number of items that have been collected. b. How many more pairs of socks than toothbrushes have been collected on day 7? 74 Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

10 Name Date Extension 3.2 Practice For use after Extension 3.2 Factor the expression using the GCF b a x y 24t 7. 10w 50z 8. 10v 12u 9. 9a 15b Factor out the coefficient of the variable a d s 6 3 Copyright Big Ideas Learning, LLC Big Ideas Math Red Accelerated Record and Practice Journal 51

11 Name Date Extension 3.2 Practice (continued) Factor out the coefficient of the variable y x c Factor 2 out of 6x Factor out of y A square window has a perimeter of 8 12 feet. x Write an expression that represents the side length of the window (in feet). 52 Big Ideas Math Red Accelerated Copyright Big Ideas Learning, LLC Record and Practice Journal

12 Name Date Extension 3.2 Practice Factor the expression using the GCF y t p s v 24w 8. 9b 24c 9. 12y 42z Factor out the coefficient of the variable m j k a f x Factor out of x 78 Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

13 17. Factor out of x y The area of the rectangle is x square inches. Write an expression that represents the length of the rectangle (in inches). 19. A concession stand sells hamburgers. The revenue from the hamburgers is 30x 45 dollars. a. The price of a hamburger is $5. Write an expression that represents the number of hamburgers sold. b. The revenue from drinks is 63x 84 dollars. The price of a drink is $3. Write an expression that represents the number of drinks sold. c. Write and simplify an expression that represents how many more drinks were sold. Copyright Big Ideas Learning, LLC Big Ideas Math 6 Record and Practice Journal 79

14 7U3L3 Name ID: 1 t Z2H0i1l5f hkluhtxam ESeomfBtNw\aArGez JL]LyCd.D D vawl]lo HrhiOgohStlsA RrYersfecravse[dV. Solving Equations Using Addition or Subtraction Solve each equation. 1) v - 8 = ) x = - 34 Date 3) b - 19 = ) k - 8 = ) - 8 = n - 5 6) m - 7 = ) - 32 = p ) - 16 = x - 13 \ U2l0_1z5q FKnuYtJa\ ^Sho[fktJw\aSrfer tlrl_ca.s r QATlBli KrKiJgihitHsQ `rfehsre\rvvdesdq.j C bm`asdwex fwyiutkhn virnrfzicnwidtbek yperdet-warlrgqejb\rxaq. -1- Worksheet by Kuta Software LLC

15 9) = x ) n = ) 31 9 = 2 + p 12) 1 + n = ) 12.2 = r ) n = ) x = ) k = z w2h0^1g5w tkvu[tiak msloofftswyalrzeu XLYLcCU.n p IAmlMlT _rbi_grhstjs^ orneusoehrjvtend`.i q MMpa`dpef AwiiUtPhZ qiinbf\imnwistben XP]rFek-EA`lIgteCbprZaR. -2- Worksheet by Kuta Software LLC

16 7U3L3 Name ID: 1 ^ y2`0k1o5l HKyuDtua_ LS`oVfZtAwtaNrdej klyl`c\.q H paglqlh oroilg]hxt_so DrHebs`ecrQvLeAds. Solving Equations Using Addition or Subtraction B Solve each equation. 1) k + 7 = 22 2) x - 15 = - 32 Date 3) b + 20 = 6 4) n - 13 = ) k - 19 = ) x + 15 = 22 7) n - 17 = ) 14 = n - 5 a O2e0Q1k5R [KGuqtgaX CSZoKfdtkwEajrgeD WLRL`CA.N w iaglzlm yrnicgqhstjsv ursewsleyrrvxebdo.y a HMiaVd\eO awziktbhr nilnbfli[nsirt]ex kp_riej-ka`lqgbelbhr\al. -1- Worksheet by Kuta Software LLC

17 9) = k ) = 16 + x 11) 37 6 = x 12) 6 = a ) 22.1 = b ) = b ) = a ) = b ` l2i0]1w5z pkvuetaak vsdo]fwtnwba_roep \LhLGC].j [ uazlila grsivgthwtdsb irfexsoeorvvnexdq.[ u jmwaedhei GwPihtOhp oifnlfuiwn\i`txet NPfrkeg-hAQlbgPeQbSrraL. -2- Worksheet by Kuta Software LLC

18 Name Date 3.3 Practice For use after Lesson 3.3 Solve the equation. Check your solution. 1. y c d n g k Write the word sentence as an equation. Then solve less than x is is the sum of a number z and A clothing company makes a profit of $2.3 million. This is $4.1 million more than last year. What was the profit last year? 56 Big Ideas Math Red Accelerated Copyright Big Ideas Learning, LLC Record and Practice Journal

19 Name Date 3.3 Practice A Solve the equation. Check your solution. 1. x b n 9 4. y x k p r m d 12 6 Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 81

20 t c Write the word sentence as an equation. Then solve more than a number y is The sum of 8 and a number h is is 4 less than a number n. In Exercises 16 20, write an equation. Then solve. 16. You earn $9 per hour babysitting. This is $2 more than what you earned per hour last year. What did you earn per hour last year? 17. Your mother asked you to turn the oven down to 325 F. This is 75 F less than it was. What was the original temperature? 82 Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

21 18. The difference between the heights of your chair and your desk is inches. The height of your desk is 29 inches. What is the 4 4 height of your chair? 19. Your Two-Day-Pass to a theme park is $ This is $31.41 less than your uncle s Two-Day-Pass. What is the price of your uncle s pass? 20. The perimeter of a triangle is 25 feet. What is the length of the unknown side? 21.Find the value of 3x 2 when 7 x 5. Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 83

22 Name Date 3.3 Practice B Solve the equation. Check your solution. 1. x g m j y z q r b d f c Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

23 Write the word sentence as an equation. Then solve is 12 more than a number x. 14. The difference of a number p and 9 is less than a number m is 72. In Exercises 16 18, write an equation. Then solve. 16. You swim the 50-meter freestyle in seconds. This is 0.14 second less than your previous fastest time. What was your previous fastest time? 17. The perimeter of a rectangular backyard is sides are each meters. The two shorter meters long. What is the length of the two longer sides? (Hint: The sum of the shorter side and the longer side is equal to half of the perimeter.) 18. The temperature of dry ice is F, which is F less than the outside temperature. What is the outside temperature? 19. Your cell phone bill in August was $61.43, which was $21.75 more than your bill in July. Your cell phone bill in July was $13.62 less than your bill in June. What was your cell phone bill in June? Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 85

24 7U3L4 Name ID: 1 x g2y0n1m5q OKTuLtjaH DSQoTfktiwUaaryeh slwlicu.q M UAml\ln MryingihStBsS brcecs_etrzvtewdm. Solving Equations Using Mult or Division A Solve each equation. Date 1) - 6k = 18 2) n 8 = 4 3) x 5 = 12 4) - 13n = ) 17n = ) = - 13a h D2W0F1l5p tkguotbab aspoffgtawlaareez DLyL]CB.l S VAHlHli Er_iPgwhQtjsI [r\efseenr_veendy._ c smnardoet Bw]iktahZ VIdnefKiCnLiRtdee MPTrxe_-LAdlHgnepbBrlaS. -1- Worksheet by Kuta Software LLC

25 7) - 2b = ) 9 = x 10 9) = - 4n 10) x = ) n = ) x = ) = - 9.4m 14) - 7.6n = 57 I o2p0d1e5t mkxugtiak bsto`fntiwmabrkey SLKLiCP.w F UAglJlR Hrci[gjhwtjsw frue_stezrrvaendi.q h zmfagdked cwoiothhh eiqnefwi]nyiktoez BPlrXeO-GAmlxgRelbprdak. -2- Worksheet by Kuta Software LLC

26 15) = m 16) x = w a2w0h1n5s MKyuctJaV nspoxfzt`wiaorley YLkLdCa.` m DAOlklQ DrUirgVhUtvsD ^reeasmexrrvaeedp.r G km`aldyeb Ewnietphy KIGnffRifn]iOt[eo mpgrjei-iaylbgkelbkrbau. -3- Worksheet by Kuta Software LLC

27 7U3L4 Name ID: 1 Y N2A0d1l5k tkzuptqat hssovflt[wcagrfec olrlmcy.q I \AZlVl` RrKiggih`t\ss dreemsbegruvreqd_. Solving Equations Using Mult or Division B Solve each equation. 1) - 19r = 190 2) - 15 p = 150 Date 3) x 15 = ) 6b = 48 5) m 5 = - 1 6) 3v = - 45 m W2g0o1m5I UKzu^trab HSDoLfttPwTaXrbem DLULQCb.h F FAclJlW Brsidg]hqtFsu VrAe`sJenrcvyecdj.E R XMHavdbe\ Zwci^tshe FIdnpfXiGnQigtFeo IPKrDeA-uAblRg_eWbhroad. -1- Worksheet by Kuta Software LLC

28 7) 15 = n 18 8) - 20v = 380 9) 5 7 x = ) = 2 3 n 11) x = 0 12) 3 5 n = ) 2.2m = r 14) 19 = 0.7 s z2h0h1[5y NKHu_tcao ssroqfntyw_avrxex LLZLcCF.z R kaxlmla hriiggzh\tnsj orlejshewrsvbezdz.c l [MVayddeZ JwCiQtuhl GI_nifei^nQiCtOe] aprrmef-oaflxgwe]bgrsau. -2- Worksheet by Kuta Software LLC

29 15) = m 16) k 16 = I ^2X0G1N5r TK]uWtoa_ gslotfotywfawrvea dlrlycn.b W wa\lkl^ xrgiwgehztfsr Ar]easweirvvmeVdr.m g xmua[doe\ twxiytfhb TInnxfji_nxiVtUeK dperzee-ja[lfgee[byr_aa. -3- Worksheet by Kuta Software LLC

30 Name Date 3.4 Practice For use after Lesson 3.4 Solve the equation. Check your solution. d x 6 5 z n h k 1.21 Write the word sentence as an equation. Then solve. 7. A number divided by 8 is The product of 12 and a number is Big Ideas Math Red Accelerated Copyright Big Ideas Learning, LLC Record and Practice Journal

31 Copyright Big Ideas Learning, LLC Big Ideas Math 6 Record and Practice Journal 61

32 Name Date 3.4 Practice A Solve the equation. Check your solution. 1. 4b n 35 y p t q d y 5 g a k j Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 87

33 Write the word sentence as an equation. Then solve. 13. A number multiplied by 1 2 is The quotient of a number and 0.2 is 2.6. In Exercises 15 19, write an equation. Then solve. 15. You earn $7.50 per hour at a fast food restaurant. You earned $ last week. How many hours did you work last week? 16. Your family took a road trip on Saturday. You were in the car for 4.5 hours and averaged 70 miles per hour. How many miles did you travel? 17. The area of a rectangle is 1 2 square inch. The length of the rectangle is 3 8 inch. What is the width of the rectangle? 18. You are in a room with other students and are asked to get in groups of 3. When finished, there are 21 groups of 3. How many students are in the room? 19. The perimeter of a square is inches. What is the side length of the square? 88 Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

34 Name Date 3.4 Practice B Solve the equation. Check your solution t p 21 q d k q d y 8 5 g c k h Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 89

35 In Exercises 13 and 14, write an equation. Then solve. 13. You order an entree for $ You pay $0.78 in taxes. What is the tax rate? 14. If a project is handed in late, you receive 8 9 of your earned points. You received 72 points on your late project. How many points did you lose? 15. Write a multiplication equation that has a solution of Write a division equation that has a solution of There are 92 students in a room. They are separated into 18 groups. How many students are in each group? How many students are not in a group? 18. A bus token costs $1.75. a. You spend $15.75 on tokens. Write and solve an equation to find how many tokens you purchase. b. If you purchase 10 tokens, you get 2 free tokens. Write and solve an equation to find the approximate reduced price of each token. c. You also receive free tokens if you purchase 20 tokens. The reduced price for each token is $1.40. Write and solve an equation to find how many free tokens you receive. 90 Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

36 7U3L5 Name ID: 1 V U2E0V1F5m wknu]t^aq QSaosfxtbwyaDrSez plollce.o J kaelolm IrJiMg`hwtGsF urfers\ekrkvoewdp. Solving Two-Step Equations A Solve each equation. 1) - 6r + 11 = 137 2) - 14 x + 13 = 279 Date 3) k 13 = - 3 4) n = - 9 5) = - 8 p ) x = 6 m v2v0u1r5^ QK[uBtlau FSCobfDtVwDaMrUeI ]LDLICv.I r uajlflw ]rsirguhftysw Er`eZsQesr^v`eYdL.P b omeandie] twtivtmht `IbnAfgi_ngiPtxeW ^PRrPeI-cAKlGgAeybjrKaa. -1- Worksheet by Kuta Software LLC

37 7) p 2 = ) - 11 = n 28 9) = p 10) = x 11) = r 12) x = ) x = ) 5.14 = x V K2g0G1b5F [KQuktyaj WSMo[fAtpw_aBraeR wljlacv.s S la\l[lv nrpimgghmtls_ WrXets]eJrVvDeUdB.G ` `MmaudUeE rwgimtzhc GIxnHfeiCnQidtueM DPRrneN-NAvlagfeMbMrsaK. -2- Worksheet by Kuta Software LLC

38 15) = p 2 16) = m 17) = x ) = n ) r 8.3 = ) a = D N2a0p1W5` hkhu`tzam askoxfftawwa]rzeg SLRLWCB.S O nawlpli KrnipgWhUtpsw wroe\smetrmvaebdp.c B zm^aad_e\ NwSiVtch] DIjnmfliXnFintaek ^P_rBeX-CAllBgMeXb]rCaa. -3- Worksheet by Kuta Software LLC

39 7U3L5 Name ID: 1 W w2p0a1c5v LKMumtUam ystojfptpwaakryen mlfl^c_.x S pavlnlh srzingjhrtksj [rpebs^etr^vme^ds. Solving Two-Step Equations B Solve each equation. 1) 6 + 7b = 20 2) x = - 2 Date 3) v = 5 4) a = ) 13 + m 9 = 16 6) x = 10 N a2v0p1p5j DKrudt[aH rsmodfrthwfaur[eb NLjLcCG.b C makl_lz Or`irgChftmsi _rjeeskemrjvieuds.f V PMaaTdBee cwaiptfhg ni[ngfhinnhietfed QP\rSeM-cAClzg[ebborPaZ. -1- Worksheet by Kuta Software LLC

40 7) n 11 = - 3 8) - 40 = x 9) = v 10) = x 11) k = ) 34 5 x = ) = 2.2n ) = 8.2b [ u2h0b1o5m [KFuhtiaZ ssrorfctlwmavrtef XLJL[Cx.L q IAvlDlZ er]idgohotasw ursemspesrdvleqda.s l SMJaodbeQ WwviRtjht JIQnFfPion_iatReR npireek-racl[gkeiboriao. -2- Worksheet by Kuta Software LLC

41 15) = a ) = n ) b = ) r = ) = p ) - 1.3b = u q2t0d1c5t dkyustkas qs_oqfstvwdafr^eh LLuLyCM.Z E SAElwlC RrDiRgvhftYsf Ur`eqsReDrsvKemdW.e J `MnaAdyeg [wnibtnhx li`ncfriznrittke\ jpmrrei-aavlkgseybsrkam. -3- Worksheet by Kuta Software LLC

42 Name Date 3.5 Practice For use after Lesson 3.5 Solve the equation. Check your solution. 1. 3a c b z n h The length of a rectangle is 3 meters less than twice its width. a. Write an equation to find the length of the rectangle. b. The length of the rectangle is 11 meters. What is the width of the rectangle? 64 Big Ideas Math Red Accelerated Copyright Big Ideas Learning, LLC Record and Practice Journal

43 Name Date 3.5 Practice A Solve the equation. Check your solution. 1. 3k p x d h r k n y b Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 93

44 j p In Exercises 13 15, write an equation. Then solve. 13. It costs $4 to enter the fair. Each ride costs $2.50. You have $ How many rides can you go on? 14. The cable company charges a monthly fee of $45. Each movie rental is $1.99. You owe $ How many movies did you rent? 15. The perimeter of the rectangle is 24 feet. What is the width of the rectangle? Solve the equation. Check your solution c 2c k ( m 1) Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

45 19. The senior class has 412 students. They are assigned to different homerooms. There are 28 students in the smallest homeroom and the remaining 12 homerooms have the same number of students. How many students are in each of the remaining 12 homerooms? 20. You purchased paint for the rooms in your house. You have 1.5 cans of paint left. You painted 4 rooms and each room required 2 cans of paint. You spilled 1 2 of a can of paint. How many cans of paint did you purchase? a. Solve the problem by working backwards. b. Solve the equation part (a)? x How does the answer compare to Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 95

46 Name Date 3.5 Practice B Solve the equation. Check your solution. 1. 5k b w n z s p t c h Big Ideas Math Red Copyright Big Ideas Learning, LLC Resources by Chapter

47 11. 1 f u In Exercises 13 and 14, write an equation. Then solve. 13. You purchased $ worth of wheels and bearings for your skateboards. The shop charges $15 per board to install them. The total cost is $ How many skateboards will be repaired? 14. A music download service charges a flat fee each month and $0.99 per download. The total cost for downloading 27 songs this month is $ How much is the flat fee? Solve the equation. Check your solution x 2x 3x m ( a 2) The perimeter of a triangle is 60 feet. One leg is 12 feet long. Of the two unknown sides, one of them is twice as long as the other. Find the lengths of the two unknown sides. Copyright Big Ideas Learning, LLC Big Ideas Math Red Resources by Chapter 97