Skip to main content
Global

2.1E: Mazoezi

  • Page ID
    177598
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Mazoezi hufanya kamili

    Thibitisha Suluhisho la Equation

    Katika mazoezi yafuatayo, onyesha kama thamani iliyotolewa ni suluhisho la equation.

    Zoezi\(\PageIndex{1}\)

    Ni\(y=\frac{5}{3}\) suluhisho la
    \(6 y+10=12 y ?\)

    Jibu

    Ndio

    Zoezi\(\PageIndex{2}\)

    Ni\(x=\frac{9}{4}\) suluhisho la
    \(4 x+9=8 x ?\)

    Zoezi\(\PageIndex{3}\)

    Ni\(u=-\frac{1}{2}\) suluhisho la
    \(8 u-1=6 u ?\)

    Jibu

    Hapana

    Zoezi\(\PageIndex{4}\)

    Ni\(v=-\frac{1}{3}\) suluhisho la
    \(9 v-2=3 v ?\)

    Kutatua Equations kwa kutumia Ondoa na Kuongeza Mali ya Usawa

    Katika mazoezi yafuatayo, tatua kila equation kwa kutumia Ondoa na Kuongeza Mali ya Usawa.

    Zoezi\(\PageIndex{5}\)

    \(x+24=35\)

    Jibu

    x = 11

    Zoezi\(\PageIndex{6}\)

    \(x+17=22\)

    Zoezi\(\PageIndex{7}\)

    \(y+45=-66\)

    Jibu

    y = -111

    Zoezi\(\PageIndex{8}\)

    \(y+39=-83\)

    Zoezi\(\PageIndex{9}\)

    \(b+\frac{1}{4}=\frac{3}{4}\)

    Jibu

    \(b = \frac{1}{2}\)

    Zoezi\(\PageIndex{10}\)

    \(a+\frac{2}{5}=\frac{4}{5}\)

    Zoezi\(\PageIndex{11}\)

    \(p+2.4=-9.3\)

    Jibu

    p = -11.7

    Zoezi\(\PageIndex{12}\)

    \(m+7.9=11.6\)

    Zoezi\(\PageIndex{13}\)

    \(a-45=76\)

    Jibu

    a = 121

    Zoezi\(\PageIndex{14}\)

    \(a-30=57\)

    Zoezi\(\PageIndex{15}\)

    \(m-18=-200\)

    Jibu

    m = -182

    Zoezi\(\PageIndex{16}\)

    \(m-12=-12\)

    Zoezi\(\PageIndex{17}\)

    \(x-\frac{1}{3}=2\)

    Jibu

    \(x=\frac{7}{3}\)

    Zoezi\(\PageIndex{18}\)

    \(x-\frac{1}{5}=4\)

    Zoezi\(\PageIndex{19}\)

    \(y-3.8=10\)

    Jibu

    y = 10.8

    Zoezi\(\PageIndex{20}\)

    \(y-7.2=5\)

    Zoezi\(\PageIndex{21}\)

    \(x-165=-420\)

    Jibu

    \(x=-255\)

    Zoezi\(\PageIndex{22}\)

    \(z-101=-314\)

    Zoezi\(\PageIndex{23}\)

    \(z+0.52=-8.5\)

    Jibu

    \(z=-9.02\)

    Zoezi\(\PageIndex{24}\)

    \(x+0.93=-4.1\)

    Zoezi\(\PageIndex{25}\)

    \(q+\frac{3}{4}=\frac{1}{2}\)

    Jibu

    \(q = -\frac{1}{4}\)

    Zoezi\(\PageIndex{26}\)

    \(p+\frac{1}{3}=\frac{5}{6}\)

    Zoezi\(\PageIndex{27}\)

    \(p-\frac{2}{5}=\frac{2}{3}\)

    Jibu

    \(p=\frac{16}{15}\)

    Zoezi\(\PageIndex{28}\)

    \(y-\frac{3}{4}=\frac{3}{5}\)

    Tatua Equations zinazohitaji kurahisisha

    Katika mazoezi yafuatayo, tatua kila equation.

    Zoezi\(\PageIndex{29}\)

    \(c+31-10=46\)

    Jibu

    c = 25

    Zoezi\(\PageIndex{30}\)

    \(m+16-28=5\)

    Zoezi\(\PageIndex{31}\)

    \(9 x+5-8 x+14=20\)

    Jibu

    x = 1

    Zoezi\(\PageIndex{32}\)

    \(6 x+8-5 x+16=32\)

    Zoezi\(\PageIndex{33}\)

    \(-6 x-11+7 x-5=-16\)

    Jibu

    x = 0

    Zoezi\(\PageIndex{34}\)

    \(-8 n-17+9 n-4=-41\)

    Zoezi\(\PageIndex{35}\)

    \(5(y-6)-4 y=-6\)

    Jibu

    \(y=8 \quad y=24\)

    Zoezi\(\PageIndex{36}\)

    \(9(y-2)-8 y=-16\)

    Zoezi\(\PageIndex{37}\)

    \(8(u+1.5)-7 u=4.9\)

    Jibu

    \(u=-7.1\)

    Zoezi\(\PageIndex{38}\)

    \(5(w+2.2)-4 w=9.3\)

    Zoezi\(\PageIndex{39}\)

    \(6 a-5(a-2)+9=-11\)

    Jibu

    \(a=-30\)

    Zoezi\(\PageIndex{40}\)

    \(8 c-7(c-3)+4=-16\)

    Zoezi\(\PageIndex{41}\)

    \(\begin{array} {l} 6(y-2)-5 y=4(y+3) \\ -4(y-1)\end{array}\)

    Jibu

    y =28

    Zoezi\(\PageIndex{42}\)

    \(\begin{array}{l}{9(x-1)-8 x=-3(x+5)} \\ {+3(x-5)}\end{array}\)

    Zoezi\(\PageIndex{43}\)

    \(\begin{array}{l}{3(5 n-1)-14 n+9} \\ {=10(n-4)-6 n-4(n+1)}\end{array}\)

    Jibu

    n = -50

    Zoezi\(\PageIndex{44}\)

    \(\begin{array}{l}{2(8 m+3)-15 m-4} \\ {=9(m+6)-2(m-1)-7 m}\end{array}\)

    Zoezi\(\PageIndex{45}\)

    \(-(j+2)+2 j-1=5\)

    Jibu

    j = 8

    Zoezi\(\PageIndex{46}\)

    \(-(k+7)+2 k+8=7\)

    Zoezi\(\PageIndex{47}\)

    \(-\left(\frac{1}{4} a-\frac{3}{4}\right)+\frac{5}{4} a=-2\)

    Jibu

    \(a=-\frac{11}{4}\)

    Zoezi\(\PageIndex{48}\)

    \(-\left(\frac{2}{3} d-\frac{1}{3}\right)+\frac{5}{3} d=-4\)

    Zoezi\(\PageIndex{49}\)

    \(\begin{array}{l}{8(4 x+5)-5(6 x)-x} \\ {=53-6(x+1)+3(2 x+2)}\end{array}\)

    Jibu

    x=13

    Zoezi\(\PageIndex{50}\)

    \(\begin{array}{l}{6(9 y-1)-10(5 y)-3 y} \\ {=22-4(2 y-12)+8(y-6)}\end{array}\)

    Tafsiri kwa Equation na Kutatua

    Katika mazoezi yafuatayo, tafsiri kwa equation na kisha kuitatua.

    Zoezi\(\PageIndex{51}\)

    Tisa zaidi ya\(x\) ni sawa na\(52 .\)

    Jibu

    \(x+9=52 ; x=43\)

    Zoezi\(\PageIndex{52}\)

    Jumla ya\(x\) na\(-15\) ni 23.

    Zoezi\(\PageIndex{53}\)

    Kumi chini ya\(m\) ni\(-14\).

    Jibu

    \(m-10=-14 ; m=-4\)

    Zoezi\(\PageIndex{54}\)

    Tatu chini ya\(y\) ni\(-19\).

    Zoezi\(\PageIndex{55}\)

    Jumla ya\(y\) na\(-30\) ni\(40 .\)

    Jibu

    \(y+(-30)=40 ; y=70\)

    Zoezi\(\PageIndex{56}\)

    Kumi na mbili zaidi\(p\) ya ni sawa na\(67 .\)

    Zoezi\(\PageIndex{57}\)

    Tofauti ya 9\(x\) na 8\(x\) ni 107.

    Jibu

    \(9 x-8 x=107 ; 107\)

    Zoezi\(\PageIndex{58}\)

    Tofauti ya 5\(c\) na 4\(c\) ni\(602 .\)

    Zoezi\(\PageIndex{59}\)

    Tofauti ya 5\(c\) na 4\(c\) ni 602

    Jibu

    \(n-\frac{1}{6}=\frac{1}{2} ; \frac{2}{3}\)

    Zoezi\(\PageIndex{60}\)

    Tofauti ya\(f\) na\(\frac{1}{3}\) ni\(\frac{1}{12}\).

    Zoezi\(\PageIndex{61}\)

    Jumla ya\(-4 n\) na 5\(n\) ni\(-82\)

    Jibu

    \(-4 n+5 n=-82 ;-82\)

    Zoezi\(\PageIndex{62}\)

    Jumla ya\(-9 m\) na 10\(m\) ni\(-95\)

    Tafsiri na Kutatua Maombi

    Katika mazoezi yafuatayo, tafsiri katika equation na kutatua.

    Zoezi\(\PageIndex{63}\)

    Umbali Avril alipanda baiskeli yake jumla ya 18 maili, kutoka nyumbani kwa maktaba na kisha pwani. Umbali kutoka nyumba ya Avril hadi maktaba ni maili 7. Ni umbali gani kutoka maktaba hadi pwani?

    Jibu

    11 maili

    Zoezi\(\PageIndex{64}\)

    Kusoma Jeff alisoma jumla ya kurasa 54 katika vitabu vyake vya Historia na Sociology. Alisoma kurasa 41 katika kitabu chake cha Historia. Alisoma kurasa ngapi katika kitabu chake cha Sociology?

    Zoezi\(\PageIndex{65}\)

    Umri binti wa Eva ni mdogo wa miaka 15 kuliko mwanawe. Mwana wa Eva ana umri wa miaka 22. Binti yake ni umri gani?

    Jibu

    Umri wa miaka 7

    Zoezi\(\PageIndex{66}\)

    Baba wa umri wa Pablo ni umri wa miaka 3 kuliko mama yake. Mama wa Pablo ana umri wa miaka 42. Baba yake ni umri gani?

    Zoezi\(\PageIndex{67}\)

    Mboga Kwa familia siku ya kuzaliwa chakula cha jioni, Celeste kununuliwa Uturuki kwamba vunja 5 paundi chini ya moja yeye kununuliwa kwa ajili ya Shukrani. Uturuki wa kuzaliwa ulikuwa na uzito wa paundi 16. Je! Uturuki wa Shukrani ulipima kiasi gani?

    Jibu

    £21

    Zoezi\(\PageIndex{68}\)

    Uzito Allie uzito 8 paundi chini ya dada yake pacha Lorrie. Allie ina uzito paundi 124. Lorrie anapima kiasi gani?

    Zoezi\(\PageIndex{69}\)

    Health Connor joto ilikuwa 0.7 digrii juu leo asubuhi kuliko ilivyokuwa jana usiku. Joto lake asubuhi hii lilikuwa digrii 101.2. Joto lake lilikuwa nini jana usiku?

    Jibu

    digrii 100.5

    Zoezi\(\PageIndex{70}\)

    Afya Muuguzi aliripoti kuwa binti wa Tricia alikuwa amepata paundi 4.2 tangu ukaguzi wake wa mwisho na sasa ana uzito wa paundi 31.6. Je! Binti wa Tricia alipima kiasi gani wakati wa ukaguzi wake wa mwisho?

    Zoezi\(\PageIndex{71}\)

    Mshahara Ron ya malipo wiki hii ilikuwa $17.43 chini ya malipo yake wiki iliyopita. Malipo yake wiki hii ilikuwa $103.76. Ni kiasi gani cha malipo ya Ron wiki iliyopita?

    Jibu

    $121.19

    Zoezi\(\PageIndex{72}\)

    Kitabu cha hesabu cha Melissa Kitabu cha gharama $22.85 chini ya gharama yake ya kitabu cha sanaa. Kitabu chake cha hesabu kiligharimu $93.75. Je! Kitabu chake cha sanaa kina gharama gani?

    kila siku Math

    Zoezi\(\PageIndex{73}\)

    Ujenzi Miguel anataka kuchimba shimo kwa screw\(\frac{5}{8}\) inch. Shimo inapaswa kuwa\(\frac{1}{12}\) inchi ndogo kuliko screw. Hebu\(d\) sawa na ukubwa wa shimo anapaswa kuchimba. Tatua\(d=\frac{5}{8}-\frac{1}{12}\) equation kuona ukubwa gani shimo lazima.

    Jibu

    \(d=\frac{13}{24}\)inchi

    Zoezi\(\PageIndex{74}\)

    Baking Kelsey mahitaji\(\frac{2}{3}\) kikombe cha sukari kwa mapishi cookie yeye anataka kufanya. Ana\(\frac{3}{8}\) kikombe cha sukari tu na
    atakopa wengine kutoka kwa jirani yake. Hebu\(s\) sawa kiasi cha sukari atakopa. Kutatua equation\(\frac{3}{8}+s=\frac{2}{3}\) kupata
    kiasi cha sukari yeye lazima kuomba kukopa.

    Mazoezi ya kuandika

    Zoezi\(\PageIndex{75}\)

    Je ufumbuzi\(-8\) wa equation\(3 x=16-5 x ?\) Unajuaje?

    Jibu

    Hapana. Haki zitatofautiana.

    Zoezi\(\PageIndex{76}\)

    Je, ni hatua ya kwanza katika ufumbuzi wako kwa equation\(10 x+2=4 x+26 ?\)

    Self Check

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

    Hii ni meza ambayo ina safu sita na nguzo nne. Katika mstari wa kwanza, ambayo ni mstari wa kichwa, seli zinasoma kutoka kushoto kwenda kulia “Ninaweza...,” “Kwa ujasiri,” “Kwa msaada fulani,” na “Hakuna-Siipati!” Safu ya kwanza chini ya “naweza...” inasomeka “kuthibitisha suluhisho la equation,” “kutatua equations kwa kutumia kuondoa na kuongeza mali ya usawa,” “kutatua milinganyo ambayo inahitaji kurahisisha,” “kutafsiri kwa equation na kutatua,” na “kutafsiri na kutatua maombi.” Wengine wa seli ni tupu.

    ⓑ Kama wengi wa hundi yako walikuwa:

    ... kwa ujasiri. Hongera! Umefanikiwa malengo yako 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 kama mada huna bwana kuwa mashimo katika barabara yako ya mafanikio. Math ni mtiririko - 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 muhimu na haipaswi kupuuza. Unahitaji kupata msaada mara moja au utazidiwa haraka. Angalia mwalimu wako haraka iwezekanavyo ili kujadili hali yako. Pamoja unaweza kuja na mpango wa kupata msaada unayohitaji.