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2.3E: Mazoezi

  • Page ID
    177584
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    Mazoezi hufanya kamili

    Tatua Equations na Constants Pande zote mbili

    Katika mazoezi yafuatayo, tatua usawa wafuatayo na mara kwa mara pande zote mbili.

    Zoezi\(\PageIndex{1}\)

    \(9 x-3=60\)

    Zoezi\(\PageIndex{2}\)

    \(12 x-8=64\)

    Jibu

    \(x=6\)

    Zoezi\(\PageIndex{3}\)

    \(14 w+5=117\)

    Zoezi\(\PageIndex{4}\)

    \(15 y+7=97\)

    Jibu

    \(y=6\)

    Zoezi\(\PageIndex{5}\)

    \(2 a+8=-28\)

    Zoezi\(\PageIndex{6}\)

    \(3 m+9=-15\)

    Jibu

    \(m=-8\)

    Zoezi\(\PageIndex{7}\)

    \(-62=8 n-6\)

    Zoezi\(\PageIndex{8}\)

    \(-77=9 b-5\)

    Jibu

    \(b=-8\)

    Zoezi\(\PageIndex{9}\)

    \(35=-13 y+9\)

    Zoezi\(\PageIndex{10}\)

    \(60=-21 x-24\)

    Jibu

    \(x=-4\)

    Zoezi\(\PageIndex{11}\)

    \(-12 p-9=9\)

    Zoezi\(\PageIndex{12}\)

    \(-14 q-2=16\)

    Jibu

    \(q=-\frac{9}{7}\)

    Tatua Ulinganisho na Vigezo Pande zote mbili

    Katika mazoezi yafuatayo, tatua usawa wafuatayo na vigezo pande zote mbili.

    Zoezi\(\PageIndex{13}\)

    \(19 z=18 z-7\)

    Zoezi\(\PageIndex{14}\)

    \(21 k=20 k-11\)

    Jibu

    \(k=-11\)

    Zoezi\(\PageIndex{15}\)

    \(9 x+36=15 x\)

    Zoezi\(\PageIndex{16}\)

    \(8 x+27=11 x\)

    Jibu

    \(x=9\)

    Zoezi\(\PageIndex{17}\)

    \(c=-3 c-20\)

    Zoezi\(\PageIndex{18}\)

    \(b=-4 b-15\)

    Jibu

    \(b=-3\)

    Zoezi\(\PageIndex{19}\)

    \(9 q=44-2 q\)

    Zoezi\(\PageIndex{20}\)

    \(5 z=39-8 z\)

    Jibu

    \(z=3\)

    Zoezi\(\PageIndex{21}\)

    \(6 y+\frac{1}{2}=5 y\)

    Zoezi\(\PageIndex{22}\)

    \(4 x+\frac{3}{4}=3 x\)

    Jibu

    \(x=-\frac{3}{4}\)

    Zoezi\(\PageIndex{23}\)

    \(-18 a-8=-22 a\)

    Zoezi\(\PageIndex{24}\)

    \(-11 r-8=-7 r\)

    Jibu

    \(r=-2\)

    Tatua Equations na Vigezo na Constants Pande zote mbili

    Katika mazoezi yafuatayo, tatua equations zifuatazo na vigezo na mara kwa mara pande zote mbili.

    Zoezi\(\PageIndex{25}\)

    \(8 x-15=7 x+3\)

    Zoezi\(\PageIndex{26}\)

    \(6 x-17=5 x+2\)

    Jibu

    \(x=19\)

    Zoezi\(\PageIndex{27}\)

    \(26+13 d=14 d+11\)

    Zoezi\(\PageIndex{28}\)

    \(21+18 f=19 f+14\)

    Jibu

    \(f=7\)

    Zoezi\(\PageIndex{29}\)

    \(2 p-1=4 p-33\)

    Zoezi\(\PageIndex{30}\)

    \(12 q-5=9 q-20\)

    Jibu

    \(q=-5\)

    Zoezi\(\PageIndex{31}\)

    \(4 a+5=-a-40\)

    Zoezi\(\PageIndex{32}\)

    \(8 c+7=-3 c-37\)

    Jibu

    \(c=-4\)

    Zoezi\(\PageIndex{33}\)

    \(5 y-30=-5 y+30\)

    Zoezi\(\PageIndex{34}\)

    \(7 x-17=-8 x+13\)

    Jibu

    \(x=2\)

    Zoezi\(\PageIndex{35}\)

    \(7 s+12=5+4 s\)

    Zoezi\(\PageIndex{36}\)

    \(9 p+14=6+4 p\)

    Jibu

    \(p=-\frac{8}{5}\)

    Zoezi\(\PageIndex{37}\)

    \(2 z-6=23-z\)

    Zoezi\(\PageIndex{38}\)

    \(3 y-4=12-y\)

    Jibu

    \(y=4\)

    Zoezi\(\PageIndex{39}\)

    \(\frac{5}{3} c-3=\frac{2}{3} c-16\)

    Zoezi\(\PageIndex{40}\)

    \(\frac{7}{4} m-7=\frac{3}{4} m-13\)

    Jibu

    \(m=-6\)

    Zoezi\(\PageIndex{41}\)

    \(8-\frac{2}{5} q=\frac{3}{5} q+6\)

    Zoezi\(\PageIndex{42}\)

    \(11-\frac{1}{5} a=\frac{4}{5} a+4\)

    Jibu

    \(a=7\)

    Zoezi\(\PageIndex{43}\)

    \(\frac{4}{3} n+9=\frac{1}{3} n-9\)

    Zoezi\(\PageIndex{44}\)

    \(\frac{5}{4} a+15=\frac{3}{4} a-5\)

    Jibu

    \(a=-40\)

    Zoezi\(\PageIndex{45}\)

    \(\frac{1}{4} y+7=\frac{3}{4} y-3\)

    Zoezi\(\PageIndex{46}\)

    \(\frac{3}{5} p+2=\frac{4}{5} p-1\)

    Jibu

    \(p=15\)

    Zoezi\(\PageIndex{47}\)

    \(14 n+8.25=9 n+19.60\)

    Zoezi\(\PageIndex{48}\)

    \(13 z+6.45=8 z+23.75\)

    Jibu

    \(z=3.46\)

    Zoezi\(\PageIndex{49}\)

    \(2.4 w-100=0.8 w+28\)

    Zoezi\(\PageIndex{50}\)

    \(2.7 w-80=1.2 w+10\)

    Jibu

    \(w=60\)

    Zoezi\(\PageIndex{51}\)

    \(5.6 r+13.1=3.5 r+57.2\)

    Zoezi\(\PageIndex{52}\)

    \(6.6 x-18.9=3.4 x+54.7\)

    Jibu

    \(x=23\)

    kila siku Math

    Zoezi\(\PageIndex{53}\)

    Tiketi za tamasha Katika tamasha la shule thamani ya jumla ya tiketi zilizouzwa ilikuwa $1506. Mwanafunzi tiketi kuuzwa kwa $6 na tiketi ya watu wazima kuuzwa kwa $9. Idadi ya tiketi za watu wazima zilizouzwa ilikuwa 5 chini ya mara 3 idadi ya tiketi za wanafunzi. Kupata idadi ya tiketi ya wanafunzi kuuzwa, s, kwa kutatua equation 6s+27s-45=1506. Kuongeza mazoezi Nakala hapa.

    Zoezi\(\PageIndex{54}\)

    Kufanya uzio Jovani ana futi 150 za uzio kufanya bustani mstatili katika mashamba yake. Anataka urefu uwe na
    futi 15 zaidi ya upana. Pata upana, w, kwa kutatua equation\(150=2 w+30+2 w\).

    Jibu

    Futi 30

    Mazoezi ya kuandika

    Zoezi\(\PageIndex{55}\)

    Tatua equation\(\frac{6}{5} y-8=\frac{1}{5} y+7\) kuelezea hatua zote za ufumbuzi wako kama katika mifano katika sehemu hii.

    Zoezi\(\PageIndex{56}\)

    Tatua equation\(10 x+14=-2 x+38\) kuelezea hatua zote za ufumbuzi wako kama katika sehemu hii.

    Jibu

    \(x=2\)Haki zitatofautiana.

    Zoezi\(\PageIndex{57}\)

    Wakati wa kutatua equation na vigezo pande zote mbili, kwa nini ni kawaida bora kuchagua upande na mgawo
    mkubwa wa kuwa “variable” upande?\(x\)

    Zoezi\(\PageIndex{58}\)

    Je ufumbuzi\(x=-2\) wa equation\(5-2 x=-4 x+1 ?\) Unajuaje?

    Jibu

    Ndiyo. Hitilafu zitatofautiana.

    Self Check

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

    Hii ni meza ambayo ina safu nne 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...” inasoma: “kutatua equation na constants pande zote mbili,” “kutatua equation na vigezo pande zote mbili,” na “kutatua equation na vigezo na constants pande zote mbili.”

    ⓑ Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?