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FOR STUDENTS ENTERING: ALGEBRA I/FUNDAMENTALS OF ALG. I &¡&ry&#ç$eßr&$eN{ June 20]ó SMCMS Porents ond Students; Altoched you willfind o pockef of molh problems lhot should be completed during the summer monlhs. WE ARE ASKING THE STUDENTS TO COMPLETE THE EVEN PROBLEMS IN THIS PACKET. AII Of the problems ore mcth concepls thot were covered during lhe 201 5-l ó school yeor in yourlyour child's mof h closs. The purpose of this summer ossignment is io help you refoin the informotion lhol wos leorned over the post 9 months. All moth closses ore siepping stones for fhe nexl closs so it is importcnt lhol knowledge is retoined from yeor lo yeor. The pocket should be completed prior lo the stort of ihe 2016-17 schoolyeor. The pocket informolion moy be token for o grode in the next school yeor. ln order to help students, moth teochers from SMCMS ond ECCHS will be ovoiloble during July ond August to help students with ony difficulty they encounler. The schedule of dotes ond times will be ovoiloble on www.eccss.orq lofer in June. Pleose conlocl Mr. Schneider of [email protected] or 834-26ó5 x214iî you hove ony quesfions. AtlenÌîan porenfs of incoming 6k groders: If your chíld îs porticipoting in fhe Summer Moth Progrom oi Sl. Morys Colholîc Elemenfory School, the moy complele fhe summer molh pocket, bul it will be optìonol. Portícipotion in lhe Summer M oth Progrom will sotisfy fhe summer moth pocket requiremenl. DATE NAME 1 lntroduction to Algebra 1-1 Variables Ob¡ect¡ve: To simplify numer¡cal expressions and evaluate variable expressions. Vocabulary . Variable A symbol, such as the letter;, Value of a variable A number that used to represent one or more numbers. a variable may represent. Variable expression An expression, such as x + 5, that contains Numerical expression, or numeral An expression, such as 6 particuÌar number, called the value of the expression. òi-ptifyiog un "*p.ession * a variable. 5, that names a Replacing a numerical expression by the simpiest name of its value. Evaluating an expression Replacing each variable by a given simplifing the rcsult. Symbols CAUTION To = (is equal to) evaluate ¿å when multipli.ca¡ion + a : (is not equal 4 and b sYmbol: ab : 4' : to) va.lue and ab or a'å (muttipþ) 5, be sure to write a 5. 1. Simplify: a. 4 + (10 - 3) b. (20 + 4) + (6 ;- 3) Sotution Simplif tþe nunerical expression(s) within parentheses fi¡st. a.4*(10-3) b.(20+4)+(6+3) ,5 + 2, 4+ 7 Example 11 -'_v- 7 Simpliry each €xpress¡on. 2.8+(30+Z) 1.5+(15-3) 4. 13-(4x2) 7.Q2-L7)x6 10. (8 x 11) - (3 x 1r) Example 2 8.(36+9)+16 ll. (24 + 6) + (30 + 2) Evaluate each expression a,. Sotution 5.(9+6)+4 Replace x 9.(18+3)+(10+5) 12.(42+?¡+1rxr¡ ifx :2andy =3. b. ry 16-(0x7) 6.9+(6+4) 3. 5ry c. (6x) - 3 with 2. Replace y with 3. Insert the multiplication symbol(s). a.ïy:2.3:6 b.5xy=5.2.3=30 c. (iír) - 3=.6."7-3 = .t2:3. =9 DATE NAME 1-1 Variables þontinued) if Evaluate'each expression 3 = : J 3r 5, ande = 0. yz l8.3xz xl 17. 6yz 2t. (u) - 6 14. 13, Example ¡ 22. (52) + 4 Evaluate each expression a. - Qy) (5x) Solution n. b. 15. xz 16.4ty 19.2q 20.7x2 23. Qù - 24. (4x) 3 I + (ay) ifx =6,y:7,and,z=4. 6.(r + z) *4 -'(v-¡) ". (lr) (2y\ \ g:q \ gJ Replacex with 6 and y with 7 and insert the multiplication symbols- 30 14 Simpli$ the expressions within pàrentheses. I6 + Subtract. b.6.(x + z) il 6.{6 + 6, Replace -r with 6 and z with 4. 4) Simplify the expressioir rvithin parentheses. 10 Multiply. 60 c. b+z) _7+4 (y-x) 7-6 Replace -r with 6, y with 7, and e with 4. 11 Simplif the numeraior and denominator. 1 Divide. Evaluate each expression - (3x) 29. 5 . (x - i) 2s. (2y) if¡ = 3, ) = 5, and z = (sx) 30. 4. (x + y) 2;6. (3y) + 0, - (62) 31. -^' *-Ð) (y - x) 27. (sy) 28. (7ò 12. \\ + ') A+z) Mixed Review Exercises Perform the indicated operâtions. l. 4.2 5. 106.4 x 1.3 2. + 6. 6.72 7.8 16.35 + - 16.07 3.9 å o '' 4 *l-10 n.f;xfr ß.åx+ M.+x+ 2 3. 2.4 + 0.6 7. 50.26 x 1.2 4. 7.3 - 5.6 8. 64 + 11.++-} 12. j.- 16. ". + O.2 9 _3 168 63 714 ÐATE NAME 1-2 Grouping Symåols Ob¡ectivè: To simpl¡fy expressions with and without group¡ng symbols. Vocabulary,fsymbols Grouping symbot A symbol used to enclose an expression that should be simplified first. Multiplication symbols are often left out of expressions with grouping symbols. For example: Parentheses 6(s - 3) : 6'2 Fraction Bar Brackets 6Ís - 37 = 10+6 9-5 6'2 i6 4 CAUTION When there are no grouping symbols, simpliff in the following order: 1. Do all multiplications and divisions in order ftom left to right. . 2. Do all additions and subaactions Example Simplify: 1 - 2) 8(5) a. SQ Solution ã, 8Q - 2) in order from left to right. b. 8Q) - 2 The parentheses tell you to simplifu 8(5) means 7 - 2 first. 8'5. 40 b. 8(7) 56 - 2 2 Do the multiplic¿tion 8.7 first. Then subtract 2. 54 Simpüfy each expression. 2. a. - 3) b. 12(5) - 3 5.a.9-6+3 b.(9-6)+3 - 1) b. 9(6) - 1. a. 9(6 1 * 5:2 b.(8+5).2 4. a, 8 a' 15+3 g,-3 Example 2 Simpli$: Sorution 18 a' 15+3 s-3 =7 12(5 3. a. 6 * 4.5 b. (6 +4).s 6- a. lZ+8+4 b.(12+8)+4 ,b' 8-5 +2 2(B -Ð Simplify the numerator and denomhator first. Then divide by 6. - 8.5+2 40+2 "' z(a - s) - 2(3) 42 6 Start to simpliry tl¡e numerator and denominator, Further simplifu the numerator and denominator Then divide by 6. 3 NAME 1*2 ÐATË Grouping Sfnbols (continued) Simplify each expression. n" 6+9 7-:2 ".#+ n.y# Example 3 ts.6'-3,-+211 M-L+ 2(9-Ð 3(5 - Bvaluate each expression if a = 6,b a.a(b+4 b.ry aSolutíon t. a(b * c) : 6(2 + 3) : 6(5) : 30 , 8(c+ð a-h o.5-4 to.ffi e.t a l1 -3 "'2+6 3) :2,c:3,ardd:O. h Replace a with 6, å with 2, and c with 3. Simplify the expression within perentheses Mulriply. 8ß +01 Replace the variables with their given values. 6-Z : -c(Ð Simplify the numerâtor and denominator. 4 24 Divide. .4 :à ¡ = 2, ! : 4, z = 6, and ó = 5. 16.a.5y- 1 17. a. 16-3b Evaluate each expression if 15. à.2ic + 5 , b. 2(x + 5) 1\a.bx*y y) 23, 5(4y - 3x) b. å(x + 27. ry x+z - Ð 20.a.n-b b. x(z - b) A. 6z - zxy b. 5(I 2s. b. (16 .- 18. a. 3z + 4. b. 3(z + 4) 3Jb 2!. a.2ry +z b. 2(xy + h. -5 2s- :,,¿ - z, 25. ryz -Er-.r z-b 5(b - -b - b) 22, a. 6ryz z) yl 6x(yz 26. x(y.y + 30. ?ry) x+y Mixed Review Exercises Simplify. 3 4.9+ 15 +3 .1. (12 - Evaluate eaeh expressiori if 7. 5ab l0.o+" c-at 2.20'8 + 18.2 S. lzs +3) + (8 +2) 6) + a= 2, b 8. 1r. = 3, and ¿ = 6. (7 + sr.(8 4. 9. (2c) bc (7a) 3.sxQ5-7) - (4b) 12. 6a - 3 - 2) z) DATE NAMË 2-3 Rules for AddÍtion Ob¡ective: To add real numbers using rules for add¡t¡on. Vocabulary sþs Opposite A positive and a negative number are said 1o have opposite signs. Examples Rules for Addition 2+5 If two numbers have lhe same sign, add their absolute values and put their common sign befo¡e the result. =7 -2+(-s)=-7 If two numbers have opposite signs, subtract the lesser absolute value 6+(-4):6-4:2 (-6)+4=-(6-4)=*2 from the greater and put the sigIt of the number having the greâter absolute value before the result. If two numbers are opposites, then their sum is zero. 3+(-3)=0 +(-9). Exañple 1 Add6 + (-8) Sotution '1 Add the numbers in order fr'om left to right. + 13 5+(-8).+13+(-9) .-2 + 13.+ (-9) + (-9), .il -.--=----..\/- !-..-ìJ+ 2 Solution 2 l. Add positilr numbers. 2. 6-8 13 Add negative numbers. 3. Add the results t9 19 -g -17 -17 '2 Ädd. 1. 6 2 -4 -7 2. 8. -35 -s6 120 3. -7 4. -3 5- 6 9. 126 10. - 14s 11. 23 6. -56 64 J1 136 12. -162 323 -35 309 _11 -58 -r7 .-82 -¿5 .47 -82 Add. 13.(-8+5)+2 L6. (-2 + 6) + (-4) 14. (-12 + 15) + 6 *5 + (-3) + s 17. ts. (-4 + 8) + (-3) 18. -4 + (-14) + 4 23 DATE NAME '2,-3 Rules for AdditiÒn þontinùed) Add. -6 + (-U) + 6 22. (-3 + 3) + 17 + (-'7) 24. -7 + (-s) + (-6) 26. -7s + 10 + (-3).+ (-2) 16+5+(-8) 21. ( 3+3)+7 +(-r1) 20. 19. 23. -2 + (-4) + (-8) 2s.-3+(-9)+7+(-5) + (-5) + (-x) +7. Example 2 Simplify 3 So¡ut¡on 3 + (-s) + (--x) + 7 : : -x _, *êjJ+ (-s) + lg__ltg :*x+ RegÌollp Ρe lerms Simpli&. 5 Simplify. 28.3+(-8)+(-y)+(-i1) 30. -5 +2a*8+7 27.-2+r+(-6)+3 29.-5+2n+3+(-3) 3I. 17+8å+( 15) + (-10) 33. 32. -(-7) + 3), + (-6) + 4 -Í6 + (-1)l + (-c) + 2 34. 3x +. V Example 3 EvaiuateÌ + y + (-2) if x = -2,andy Solution l : : + }' + (-2) 5.+ (-2) "+ + .3 \.-.--------v- t?, (-2) : Eraluate each expression if 35.y+z+ (-2) 37. -11. + ( -:r) 39. 1+(-])+r + (-y) 1 : + (-2) + (-3)l 5. Substitute -2 forr and 5 for y. Add from left to right. Shirplify. ¡= -2,y = 5, andz = -3. 36. -18+r+) -z + (-7) + y 40. -x + (-y) + (-15). 38. Mixed Review Exercises Simplify. 2.7.5'3.2 1.3+8{-2 4. l-el - 7 -t' 9,6+9.4 6* z 10. Uz + 24 (-2)l + 5 s. l-1.61 + r.6 3. (9 - 6 + 3)'2 6. l-111 l-sl s.:|+|+$ 9.2.7+1.0+3.3 11. (-7 + 2) + (-3) - 12.-2+(-8)+7+(-1) DATE NAME 2-4 Subtracting Reat Numbers express¡ons involving differences' To subtract real numbers and to simplity Obiective: Definition of Subtract¡ón opposiæ of b' To subtract a real number b, add the ã-b=a+(-b) ForexamPle,3 - 9 = 3 + (-9) = -6' b'-6-3 SimplifY: a'2-7 Examqle 1 1 - (- 8) a.2-7:2+(-7)=-5 b. -6- 3¿ -6+ (-3) = -9 c.-2-(-8):-2+8:6 Sorufion cAuTloN c. -2 Subtractio¡ is n¿, coÍ)rnutative ' 7 -3:4' btt3-7=-4, so7-3+3-7 CAUTION 2 Subtraction is zof âssociative' 0 -3') -2:4-2=2' - (3 - 2\ :7 - 1 = 6' so(7 - 3) -2+7 -(3 -2) uutì SimplifY' ?2. -15 24. 26. s6 - 5.0-5 8.-8-1 11. -8 - (-3) t4.36 - (-34) (4s 23. -8 25. n. 32) - (-24) (-15) - 3.5 zr. 2.65 - (-2.35) 28.214-(54-66) 30. (25 - 32) 32, (z - 7) - -3 - - !9. -2.3 -2 - ts. -2s 17. decreased bY 5 18 lebs than 3.9-13 6. 0 - (-3) 9.3 - (-3) t2. 36 - 216 2. 17 -11 -9 4.6-16 7. -12-0 x0. 7 - (-5) L3. 7ß - no 16. -ls - (-3) 18. -17 - (-8) 29. -4.2 - 5-6 1,25 (44 - Grz + s5) 15) - decreased bY 10 less than 29. J.67 31. (46 33. (32 L25 -i4 -6 - 35) QO - 4s) so) - (6s - 40) 24) - (-6 + 9) (160 25 NAME DATE 2-4 Subtracting Rèal Numbers Gantjnugd) " Example 2 Simpli{13-9-8+5.' Solutlon 13-9-8+5=13-9-8+5 =i3+(-9)+(_8)+5 + (-8)+5 .4 \-,, -* - = *ì 1 Sürplify. 34.3-4+7-15+21 36.-5-18+6_7+10 14- 12+ 11 +3 _20 37. -9 -.21 +3 -8 +30 35. Êxample 3 Simpli$: a. -(x - 5) b. _(3 _ y) c. _(_2 + a) Solution To find the opposite of a sum or a difference, you change the sign of each term the sum or difference. ã- -(n-5)= -¡+5 b. _(3 of _y): _3+y c. -(-2*a):2-o Simplify. 38. -(x + 2) 42. -(y - s) 39. -(4 43. -(8 - y) - r) Example 4 SimplifS-(,x+3). Solut¡on 8 - + 3) = 8 -* (.r -(-7 + a) 44. -(b - 6) 40. - 3 =(8_3)_f =5 -¡ 41. -(x 45. -Q + n) Change the sign of each term of.x Regroup the terms. * - 3) 3 Simplig,. Simplify. 46.6-(J+4) 47.4-(q_6) Mixed Review Exercises 1. l-61 + l2l , l-åi- l-+i 7. ls + (-9)1 + 7 10. -2.4 + s.3 + (-3.6) 26 48,x-(x+2) 2.r7.2.3.s 3.2*6x+5y*8 . (-+) '. -+* 8. 3.4 11,. 0.5 + (_i.4) -27 + (-28) + 49.n-(_3+n) 18 + 47 o. 11 4 + /-aa\ \ -4/ 9. *4 + [-6 + (-2)] 12. 2 + (-3) + (-10) + (-x) DATE NAME 2-6 Rules for Multiplication Ob¡ective: To multiply real numbers. Examples Pmperties Identity Property of Mültiplication The product of a number and to the number itself, a,1 = a I is identical and l'a: the product itself is zero. 6.0=0 and 0.6:0 and (-1)6: -6 -6 6(-1) = (*5X-1):-(-5)=s For every ¡eal number a: -a 1.6:6 and 0'¿:0 Multiplication Property of -:1 a(-l): and a Multiplication hoperty of Zem When one of the factors of a pìoduct is zero, a.0=O 6.1:6 and (- i)(-s) and (- l)a = -a Property of Opposites in Products ' For all real numbers ¿ and å: (-4X5) : -(-s) : : s -20 4(-s) : .20 (-4)(-5) :20 (-a)(b) : -ab a(-b) : -o5 (-a)(-b) : ab Rules for Multiplicat¡on 1. If two numbers h^\e If sign, lheir product ispositive. two numbers have opposite signs, their product is negative. r}re same 2. The product of a¡ svez number of negative numbers is positive. The product of an odd ntnúer of rrcgative numbers is negative. Example 1 SaJution Multiply: a. 3(6) a.3(6):18 b. (-3)(6) : -16 c. 3(-6) : -18 d. (-3x-6) : 18 Examptre 2 b. (-3X6) c. 3(-6) @oth factors have the same d. (-3)(-6) sþ.) (The two factors have opposite signs.). (The two factors have opposite signs-) (Both factors have the same sign.) a. 2(-3)(-4)(-5) is negative because it has 3 negative factors. b. (- lX-4X -5)(6X -7) is positive because it has 4 negative factors. c. (-6X7X0X-4) is zero because it has a zero facfor. to NAME '2-6 DATE Rules íor Multiplication þont¡nued) Multipty. 1. (-12X-3) 2. 18(-4) 6. (4X-7)(10) s. (-2)(sx-8) 9. 35(-26X0) 10. s(-2x-8x-s) 4. 18(0) 8. (-1rX-12X0) 3. 2(t"t) 7. (-2)(-3)(-4) 11. (-7X3X-1X2) Exainple 3 Simpli$: a, (-2.x)(-6y) b. 3y + (-7y) So/utio', a. (-2x)(-6y) : : : b. 3y + (-7¡,) (-2)x(-6)y (_2)(_6)xy lbcy 12. : : : (-8X-5X-lX-3) t3 + (-T)ly (-4)y *4y Simplify. 13. (-3a)(-4b) L4. (sx)(6y) 18. -7a 'r (-8ø) 19. 2x + (-5x) ts. 2p(-5q) 20, 8x + (-3x) 4 Simpliff: . t. -3Qx - y) Sotuf¡on a. -3(7x - )) : -9@Ð -. (-3)(y) t6. (-4e)(7Í) 27. (-Ily) + 17. (-6a)(-sb) 3y 22. -4n i 4n b.5x-4(r-1) Example b. 5x - _6x _ (_3y) = __6x+3y 4(x - (4x -.4. =5x-(4x-4) =5x-4x14 =x*4 ¡- 1) 1 5-r. Simplify. 23. 6(x * 2y) ?-6. -l(ay - 5) ?9. 4x - 3(x - Z) 32.(-1)(a-b+2) 35.4x-2,x*74x 24. -SQc + d) 27. (3x - s)(-6) 30. 6r - 2(x + 3) 33.(-1X2r-)-3) 36.2y-5-5y+3 25. -4Qm + 2n) 2.8. (-3 + 5y)(-2) 31. 3x - 5(¡ - 1) 34.(-L)(x+y-2.) 37. 1lp -6c -7c +9p Mixed Review Exercises ïlanslate each seutence into an equation. 1. Three times a number is 27. 2. The quotient of z and 4 is 15. 3. One half of a number is nine. 4. Six less than twice a number is 14. Simplify. 5. 1r0 - 8. 3(20 + 30 (12 5) - 8) 6. 161 - (8 9. 2n + (-5n) 11) 7. 2.+ (*s) + 10,5(n+1)+7 (-y) + 9 1) NAME DATE :,.;i 3 Solving Equations and Problems 3-1 Transtorming Obiective: Eqwations: Additiøn and Subtraction To solve equat¡ons using add¡tion and subtraction. Properties Addition Property of Equality If the same number is added to equal numbers, the sums are equal. Subtraction Property of Equality If the same number is subtracted from equal numbers, the differences are equal. Vocabulary Equivalent equatioru Equations that have tle same solution set over a given domain. Transformations Operâtions on an equation that produce a simpler equivalent equation. By substitution You can substitute an equivalent expression for any expression il an equation. You do this when you simpliff an expression in an equatiou. By addition You can add the same number to each side of an equation. Ey subtrâction You car suútract the same number from each side of an equation. cAUTloN Example Tb check your work, you should check that each solution of the final equation satisfies the onþzal equation. 1 Solution Solve¡-6:11. x-6:!1 x-616:11.+6 x:L7 Check: x 77 - 6: ,| 6 ,:. 11 11+11 :11 V To get x alone on one side, add 6 to each side and then simpli$r. O¡iginal equation. Substitute 17 for*. The solution set is {17}. Solve. 1.a-9=11 4.d-14=5 7. x - 6 :27 2.b-5:13 5.¡-15=0 Lq-7=11 3.x-20=-19 6.v-27:-54 9.q-9:-16 37 DATE NAME Tänsfôlf'ning Equations: Addltlon and SubtrcetiÐn' 3-1 Exanple 2 Solve-9:n*11 Sorution '9=n*11 -9-11 :z*1I -20 = Check: n [To get n alone on one side, lsubtract 11 from each side. Simplifu. 11 -9 = n * lI.- -s :2 -9 -zo + -9 \i (continaed)' Original equation 1l subsritute -2o for n. The soiution set is { -20} Solve. 10. -6:m+6 ll.2l:x+15 p+ 15:d+60=-15 = -22' 18. 35 -;r + 16 14. 18 79. 23. 22.x+1.5:6.8 Example 3 Solution Solve -4:u-6 -26+m:24 16. 14+r=0 2¡.22=y+3 -1 +a=0.5 24.3.9=y-r.4 -x -l 5 : 4. -x*5:4 -¡ 5 - 5.:.4 1- Check: n: 63 - 72 21.¿-8:-10 25. 7.5 : w - 2.5 13. -37 + 1'7. 29 = y 12. 5 . -x+ 5 =4 .--1 +5!4 4 = 4.,1 JTo get -r alone on one side, Isr.rbl¡act 5.from.each side anct simplify. ilf the opposite of a number is -1, Ithe number must be l - O¡iginal equation Subsritute I for ï. The solution set is {1} Solve. -x+3=5 29.7 -y:11 32.-5-y=7 x: 18 31. 13 =22-y -y+7:17 30.9:-x+16 33. 10= -12-e 28. 12 - 27. 26. 34.t5=_y+10 Mixed Review Exercises Eraluateif¿ = 3, b t. a-lb- cl , a-2b 4.-.'.a+d = -6, c = -4, and.d = 2. z. (lcl - d) - 3bIc-d - (ltl - o) tt. tul 38 * (-å) zab c+d - Simplify. 7. (-3X-4X8) 3.3lcl 8. (-7 - 1.6) + (-7 .24\ 9. 252 : (-36) DATE NAME 3-2 Transforming Equations: Multiplìcation anp Division Ob¡ective: To solve equations using multipl¡cation or d¡vis¡on. Properties ' Multiplication Property of Equality If equal numbers are multiplied by the . same number, the products are equal. Division Property of Equality If equal numbers are divided by the same nonzero rnmber, the quotients are equal. Transformations By multiplication You can multþ1y each side of an equationby lhe By division You can divide each side of an equation by CAUTION I same nonzera real number The s?lrîe non¿ero real number. When you transform an equation, never multiply or divide bY zero. CAUTION 2 Example lVhen you multiply or divide by a negative number, be careful with the sign of your answer. 1 Solve Solution : 4x 4r 128. 128 [To get x atone on one side, divìde each side lby 4 (or multiply by , the reciprocal of 4) 44 x:32 Check: 4x: a}z¡ f 128 ! ns 128 : 128 The solution set is {32} "l Solve. : l. 7m 4. 7. = -r43 108 = -9x 2. l2n 140 *rlf : 3. -8.x = 240 5. -720 : -245 8. 45k : -270 t2 96 6. 330 : -l5u 9. 26n = -570 : -in. Example 2 Solve Solufion -*ozt: -+(-+,) -16:n Check: 12 12 get n alone on one side, multiply each [To \43 by Iside -5, the reciprocal of -;. : -]n =')7 -iG16) . rz - 1õ tL\l I Ttre solution set is {-16} 39 NAME 3-2 DATE T ransloltnr' ing' Eguatl õns : M ultiiilicatícn end Ðívisiori Solve. n.lm=s n. -!t 16. ¡r = -zo 3 Sorufion 4v u. ?d = -40 n. -|x = +o s. |e = -24 -Is n. -l6e = Mo = -s6 Example : 11. Solve: a. ß. -ln = -zt ^i rt I b. 1:-o (contirtuêd) în I 2\t) = 2(-6) ' x: -12 ^/ 1 \ ,(+) '\1)" n T, Lheck: ¿ = -o *z-u 7 t"i Check: 1 -6: -6J The solution set is 7 2 2n 2 ?1 -2 ') (7) 7 2 {-12} 7 2 7 2 The solution set is {7} Solve. i : -24 22. -t = t5 Le. zs. Ir)" = z!J 20. + = -zs zt. -# : t2 23. -28: + z+. -tx = zt ze. !ø = zrJ- zt. -Iy J' = tZJ Mixed Review Exercises Evaluateif¿: -2,b = 3,andc: -6; l. 6b - ?a 2. Qb - 5c)a a. lbl - la + cl.. s. -0:b\ c 3. lcl+lal-b - 8+a ô.c Simplift. 7.6a*5I7a I0. -3(m + 4) 40 8.7n-6+6 11. (r + 5)6 9,9p-p+3 12.2(3y - 4)