Whakaoti i te (28/48+24.5/50x/48+52)*0.1+8/10*0.15+frac{15}{30}*0.75=0.5

$$( \frac{ 28 }{ 48 } + \frac{ 24.5 }{ 50 } \frac{ x }{ 48+52 } ) \times 0.1+ \frac{ 8 }{ 10 } \times 0.15+ \frac{ 15 }{ 30 } \times 0.75=0.5$$

Whakaoti mō x

$$x = -\frac{16000}{147} = -108\frac{124}{147} \approx -108.843537415$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{28}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\left(\frac{7}{12}+\frac{24.5}{50}\times \frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Whakarohaina te \frac{24.5}{50} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\left(\frac{7}{12}+\frac{245}{500}\times \frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Whakahekea te hautanga \frac{245}{500} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\left(\frac{7}{12}+\frac{49}{100}\times \frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Tāpirihia te 48 ki te 52, ka 100.

$$\left(\frac{7}{12}+\frac{49}{100}\times \frac{x}{100}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Me whakarea te \frac{49}{100} ki te \frac{x}{100} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\left(\frac{7}{12}+\frac{49x}{100\times 100}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 12 me 100\times 100 ko 30000. Whakareatia \frac{7}{12} ki te \frac{2500}{2500}. Whakareatia \frac{49x}{100\times 100} ki te \frac{3}{3}.

$$\left(\frac{7\times 2500}{30000}+\frac{3\times 49x}{30000}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Tā te mea he rite te tauraro o \frac{7\times 2500}{30000} me \frac{3\times 49x}{30000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7\times 2500+3\times 49x}{30000}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Mahia ngā whakarea i roto o 7\times 2500+3\times 49x.

$$\frac{17500+147x}{30000}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Whakahekea te hautanga \frac{8}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{17500+147x}{30000}\times 0.1+\frac{4}{5}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Me tahuri ki tau ā-ira 0.15 ki te hautau \frac{15}{100}. Whakahekea te hautanga \frac{15}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{17500+147x}{30000}\times 0.1+\frac{4}{5}\times \frac{3}{20}+\frac{15}{30}\times 0.75=0.5$$

Me whakarea te \frac{4}{5} ki te \frac{3}{20} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{17500+147x}{30000}\times 0.1+\frac{4\times 3}{5\times 20}+\frac{15}{30}\times 0.75=0.5$$

Mahia ngā whakarea i roto i te hautanga \frac{4\times 3}{5\times 20}.

$$\frac{17500+147x}{30000}\times 0.1+\frac{12}{100}+\frac{15}{30}\times 0.75=0.5$$

Whakahekea te hautanga \frac{12}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{15}{30}\times 0.75=0.5$$

Whakahekea te hautanga \frac{15}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 15.

$$\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{1}{2}\times 0.75=0.5$$

Me tahuri ki tau ā-ira 0.75 ki te hautau \frac{75}{100}. Whakahekea te hautanga \frac{75}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{1}{2}\times \frac{3}{4}=0.5$$

Me whakarea te \frac{1}{2} ki te \frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{1\times 3}{2\times 4}=0.5$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3}{2\times 4}.

$$\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{3}{8}=0.5$$

Ko te maha noa iti rawa atu o 25 me 8 ko 200. Me tahuri \frac{3}{25} me \frac{3}{8} ki te hautau me te tautūnga 200.

$$\frac{17500+147x}{30000}\times 0.1+\frac{24}{200}+\frac{75}{200}=0.5$$

Tā te mea he rite te tauraro o \frac{24}{200} me \frac{75}{200}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{17500+147x}{30000}\times 0.1+\frac{24+75}{200}=0.5$$

Tāpirihia te 24 ki te 75, ka 99.

$$\frac{17500+147x}{30000}\times 0.1+\frac{99}{200}=0.5$$

Whakawehea ia wā o 17500+147x ki te 30000, kia riro ko \frac{7}{12}+\frac{49}{10000}x.

$$\left(\frac{7}{12}+\frac{49}{10000}x\right)\times 0.1+\frac{99}{200}=0.5$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{7}{12}+\frac{49}{10000}x ki te 0.1.

$$\frac{7}{12}\times 0.1+\frac{49}{10000}x\times 0.1+\frac{99}{200}=0.5$$

Me tahuri ki tau ā-ira 0.1 ki te hautau \frac{1}{10}.

$$\frac{7}{12}\times \frac{1}{10}+\frac{49}{10000}x\times 0.1+\frac{99}{200}=0.5$$

Me whakarea te \frac{7}{12} ki te \frac{1}{10} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7\times 1}{12\times 10}+\frac{49}{10000}x\times 0.1+\frac{99}{200}=0.5$$

Mahia ngā whakarea i roto i te hautanga \frac{7\times 1}{12\times 10}.

$$\frac{7}{120}+\frac{49}{10000}x\times 0.1+\frac{99}{200}=0.5$$

Me tahuri ki tau ā-ira 0.1 ki te hautau \frac{1}{10}.

$$\frac{7}{120}+\frac{49}{10000}x\times \frac{1}{10}+\frac{99}{200}=0.5$$

Me whakarea te \frac{49}{10000} ki te \frac{1}{10} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7}{120}+\frac{49\times 1}{10000\times 10}x+\frac{99}{200}=0.5$$

Mahia ngā whakarea i roto i te hautanga \frac{49\times 1}{10000\times 10}.

$$\frac{7}{120}+\frac{49}{100000}x+\frac{99}{200}=0.5$$

Ko te maha noa iti rawa atu o 120 me 200 ko 600. Me tahuri \frac{7}{120} me \frac{99}{200} ki te hautau me te tautūnga 600.

$$\frac{35}{600}+\frac{49}{100000}x+\frac{297}{600}=0.5$$

Tā te mea he rite te tauraro o \frac{35}{600} me \frac{297}{600}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{35+297}{600}+\frac{49}{100000}x=0.5$$

Tāpirihia te 35 ki te 297, ka 332.

$$\frac{332}{600}+\frac{49}{100000}x=0.5$$

Whakahekea te hautanga \frac{332}{600} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{83}{150}+\frac{49}{100000}x=0.5$$

Tangohia te \frac{83}{150} mai i ngā taha e rua.

$$\frac{49}{100000}x=0.5-\frac{83}{150}$$

Me tahuri ki tau ā-ira 0.5 ki te hautau \frac{5}{10}. Whakahekea te hautanga \frac{5}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{49}{100000}x=\frac{1}{2}-\frac{83}{150}$$

Ko te maha noa iti rawa atu o 2 me 150 ko 150. Me tahuri \frac{1}{2} me \frac{83}{150} ki te hautau me te tautūnga 150.

$$\frac{49}{100000}x=\frac{75}{150}-\frac{83}{150}$$

Tā te mea he rite te tauraro o \frac{75}{150} me \frac{83}{150}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{49}{100000}x=\frac{75-83}{150}$$

Tangohia te 83 i te 75, ka -8.

$$\frac{49}{100000}x=\frac{-8}{150}$$

Whakahekea te hautanga \frac{-8}{150} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{49}{100000}x=-\frac{4}{75}$$

Me whakarea ngā taha e rua ki te \frac{100000}{49}, te tau utu o \frac{49}{100000}.

$$x=-\frac{4}{75}\times \frac{100000}{49}$$

Me whakarea te -\frac{4}{75} ki te \frac{100000}{49} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-4\times 100000}{75\times 49}$$

Mahia ngā whakarea i roto i te hautanga \frac{-4\times 100000}{75\times 49}.

$$x=\frac{-400000}{3675}$$

Whakahekea te hautanga \frac{-400000}{3675} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$x=-\frac{16000}{147}$$