2.2E: Tumia Mkakati Mkuu wa Kutatua Equations Linear (Mazoezi)

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Mazoezi hufanya kamili

Kutatua Equations Kutumia Mkakati Mkuu

Katika mazoezi yafuatayo, onyesha kama maadili yaliyotolewa ni ufumbuzi wa equation.

1. $6y+10=12y$

a.$y=\frac{5}{3}$

b.$y=−\frac{1}{2}$

Jibu: a. ndiyo
b. hapana

2. $4x+9=8x$

a.$x=−\frac{7}{8}$

b.$x=\frac{9}{4}$

3. $8u−1=6u$

a.$u=−\frac{1}{2}$

b.$u=\frac{1}{2}$

Jibu: a. hapana
b. ndiyo

4. $9v−2=3v$

a.$v=−\frac{1}{3}$

b.$v=\frac{1}{3}$

Katika mazoezi yafuatayo, tatua kila equation linear.

5. $15(y−9)=−60$

Jibu: $y=5$

6. $−16(3n+4)=32$

7. $−(w−12)=30$

Jibu: $w=−18$

8. $−(t−19)=28$

9. $51+5(4−q)=56$

Jibu: $q=3$

10. $−6+6(5−k)=15$

11. $3(10−2x)+54=0$

Jibu: $x=14$

12. $−2(11−7x)+54=4$

13. $\frac{2}{3}(9c−3)=22$

Jibu: $c=4$

14. $\frac{3}{5}(10x−5)=27$

15. $\frac{1}{5}(15c+10)=c+7$

Jibu: $c=\frac{5}{2}$

16. $\frac{1}{4}(20d+12)=d+7$

17. $3(4n−1)−2=8n+3$

Jibu: $n=2$

18. $9(2m−3)−8=4m+7$

19. $12+2(5−3y)=−9(y−1)−2$

Jibu: $y=−5$

20. $−15+4(2−5y)=−7(y−4)+4$

21. $5+6(3s−5)=−3+2(8s−1)$

Jibu: $s=10$

22. $−12+8(x−5)=−4+3(5x−2)$

23. $4(p−4)−(p+7)=5(p−3)$

Jibu: $p=−4$

24. $3(a−2)−(a+6)=4(a−1)$

25. $4[5−8(4c−3)]=12(1−13c)−8$

Jibu: $c=−4$

26. $5[9−2(6d−1)]=11(4−10d)−139$

27. $3[−9+8(4h−3)]=2(5−12h)−19$

Jibu: $h=\frac{3}{4}$

28. $3[−14+2(15k−6)]=8(3−5k)−24$

29. $5[2(m+4)+8(m−7)]=2[3(5+m)−(21−3m)]$

Jibu: $m=6$

30. $10[5(n+1)+4(n−1)]=11[7(5+n)−(25−3n)]$

Kuainisha milinganyo

Katika mazoezi yafuatayo, ainisha kila equation kama equation masharti, utambulisho, au utata na kisha hali ya ufumbuzi.

31. $23z+19=3(5z−9)+8z+46$

Jibu: utambulisho; namba zote halisi

32. $15y+32=2(10y−7)−5y+46$

33. $18(5j−1)+29=47$

Jibu: equation ya masharti;$j=\frac{2}{5}$

34. $24(3d−4)+100=52$

35. $22(3m−4)=8(2m+9)$

Jibu: equation ya masharti;$m=165$

36. $30(2n−1)=5(10n+8)$

37. $7v+42=11(3v+8)−2(13v−1)$

Jibu: utata; hakuna suluhisho

38. $18u−51=9(4u+5)−6(3u−10)$

39. $45(3y−2)=9(15y−6)$

Jibu: utata; hakuna suluhisho

40. $60(2x−1)=15(8x+5)$

41. $9(14d+9)+4d=13(10d+6)+3$

Jibu: utambulisho; namba zote halisi

42. $11(8c+5)−8c=2(40c+25)+5$

Tatua equations na Fraction au Coefficients Decimal

Katika mazoezi yafuatayo, tatua kila equation na coefficients sehemu.

43. $\frac{1}{4}x−\frac{1}{2}=−\frac{3}{4}$

Jibu: $x=−1$

44. $\frac{3}{4}x−\frac{1}{2}=\frac{1}{4}$

45. $\frac{5}{6}y−\frac{2}{3}=−\frac{3}{2}$

Jibu: $y=−1$

46. $\frac{5}{6}y−\frac{1}{3}=−\frac{7}{6}$

47. $\frac{1}{2}a+\frac{3}{8}=\frac{3}{4}$

Jibu: $a=\frac{3}{4}$

48. $\frac{5}{8}b+\frac{1}{2}=−\frac{3}{4}$

49. $2=\frac{1}{3}x−\frac{1}{2}x+\frac{2}{3}x$

Jibu: $x=4$

50. $2=\frac{3}{5}x−\frac{1}{3}x+\frac{2}{5}x$

51. $\frac{1}{3}w+\frac{5}{4}=w−\frac{1}{4}$

Jibu: $w=\frac{9}{4}$

52. $\frac{1}{2}a−\frac{1}{4}=\frac{1}{6}a+\frac{1}{12}$

53. $\frac{1}{3}b+\frac{1}{5}=\frac{2}{5}b−\frac{3}{5}$

Jibu: $b=12$

54. $\frac{1}{3}x+\frac{2}{5}=\frac{1}{5}x−\frac{2}{5}$

55. $\frac{1}{4}(p−7)=\frac{1}{3}(p+5)$

Jibu: $p=−41$

56. $\frac{1}{5}(q+3)=\frac{1}{2}(q−3)$

57. $\frac{1}{2}(x+4)=\frac{3}{4}$

Jibu: $x=−\frac{5}{2}$

58. $\frac{1}{3}(x+5)=\frac{5}{6}$

59. $\dfrac{4n+8}{4}=\dfrac{n}{3}$

Jibu: $n=−3$

60. $\dfrac{3p+6}{3}=\dfrac{p}{2}$

61. $\dfrac{3x+4}{2}+1=\dfrac{5x+10}{8}$

Jibu: $x=−2$

62. $\dfrac{10y−2}{3}+3=\dfrac{10y+1}{9}$

63. $\dfrac{7u−1}{4}−1=\dfrac{4u+8}{5}$

Jibu: $u=3$

64. $\dfrac{3v−6}{2}+5=\dfrac{11v−4}{5}$

Katika mazoezi yafuatayo, tatua kila equation na coefficients decimal.

65. $0.4x+0.6=0.5x−1.2$

Jibu: $x=18$

66. $0.7x+0.4=0.6x+2.4$

67. $0.9x−1.25=0.75x+1.75$

Jibu: $x=20$

68. $1.2x−0.91=0.8x+2.29$

69. $0.05n+0.10(n+8)=2.15$

Jibu: $n=9$

70. $0.05n+0.10(n+7)=3.55$

71. $0.10d+0.25(d+5)=4.05$

Jibu: $d=8$

72. $0.10d+0.25(d+7)=5.25$

kila siku Math

73. Uzio Micah una futi 74 za uzio wa kufanya mbwa kukimbia katika yadi yake. Anataka urefu uwe na futi 2.5 zaidi ya upana. Pata urefu, L, kwa kutatua equation$2L+2(L−2.5)=74$.

Jibu: $L=19.75$miguu

74. Mihuri Paula kununuliwa $22.82 yenye thamani ya mihuri 49-asilimia na mihuri 21 asilimia. Idadi ya mihuri ya asilimia 21 ilikuwa chini ya nane kuliko idadi ya mihuri ya asilimia 49. Kutatua equation$0.49s+0.21 (s−8) =22.82$ kwa s, kupata idadi ya 49-asilimia mihuri Paula kununuliwa.

Mazoezi ya kuandika

75. Kutumia maneno yako mwenyewe, weka hatua katika mkakati wa jumla wa kutatua equations linear.

Jibu: Majibu yatatofautiana.

76. Eleza kwa nini unapaswa kurahisisha pande zote mbili za equation iwezekanavyo kabla ya kukusanya maneno ya kutofautiana kwa upande mmoja na masharti ya mara kwa mara kwa upande mwingine.

77. Ni hatua gani ya kwanza ya kuchukua wakati wa kutatua equation$3−7(y−4)=38?$ Kwa nini hii ni hatua yako ya kwanza?

Jibu: Majibu yatatofautiana.

78. Ikiwa equation ina sehemu ndogo, kuzidisha pande zote mbili na LCD hufanya iwe rahisi kutatua?

79. Ikiwa equation ina sehemu ndogo tu upande mmoja, kwa nini unapaswa kuzidisha pande zote mbili za equation na LCD?

Jibu: Majibu yatatofautiana.

80. Kwa equation$0.35x+2.1=3.85$, jinsi gani unaweza wazi decimal?

Self Check

Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

$Jedwali hili lina nguzo nne na safu nne. Mstari wa kwanza ni kichwa na huandika kila safu, “Siwezi...”, “Kwa ujasiri,” “Kwa msaada fulani,” na “Hakuna-Siipati!” mfululizo 2, naweza mara kutatua equations linear kutumia mkakati wa jumla. mfululizo 3, naweza mara classify milinganyo. Katika mstari wa 4, naweza mara kutatua equations na sehemu au coefficients decimal.$

b Kama wengi wa hundi yako walikuwa:

... kwa ujasiri. Hongera! Umefanikiwa malengo katika sehemu hii. Fikiria ujuzi wa kujifunza uliyotumia ili uweze kuendelea kuitumia. Ulifanya nini ili uwe na ujasiri wa uwezo wako wa kufanya mambo haya? Kuwa maalum.

... kwa msaada fulani. Hii lazima kushughulikiwa haraka kwa sababu mada huna bwana kuwa mashimo katika barabara yako ya mafanikio. Katika hesabu kila mada hujenga juu ya kazi ya awali. Ni muhimu kuhakikisha kuwa na msingi imara kabla ya kuendelea. Nani unaweza kuomba msaada? Washiriki wenzako na mwalimu ni rasilimali nzuri. Je, kuna mahali kwenye chuo ambapo waalimu hisabati zinapatikana? Je, ujuzi wako wa kujifunza unaweza kuboreshwa?

... hapana - Siipati! Hii ni ishara ya onyo na haipaswi kupuuza. Unapaswa kupata msaada mara moja au utazidiwa haraka. Angalia mwalimu wako haraka iwezekanavyo kujadili hali yako. Pamoja unaweza kuja na mpango wa kupata msaada unayohitaji.