Whakaoti i te 28/48*0.025+24.5/50*0.025+x/48+52*0.05+8/10*0.15+frac{12}{30}*0.75>0.5

$$\frac{ 28 }{ 48 } \times 0.025+ \frac{ 24.5 }{ 50 } \times 0.025+ \frac{ x }{ 48+52 } \times 0.05+ \frac{ 8 }{ 10 } \times 0.15+ \frac{ 12 }{ 30 } \times 0.75 > 0.5$$

Whakaoti mō x

$$x>\frac{319}{3}$$

Ngā Upane Otinga

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

$$\frac{7}{12}\times 0.025+\frac{24.5}{50}\times 0.025+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Me tahuri ki tau ā-ira 0.025 ki te hautau \frac{25}{1000}. Whakahekea te hautanga \frac{25}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\frac{7}{12}\times \frac{1}{40}+\frac{24.5}{50}\times 0.025+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Me whakarea te \frac{7}{12} ki te \frac{1}{40} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7\times 1}{12\times 40}+\frac{24.5}{50}\times 0.025+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Mahia ngā whakarea i roto i te hautanga \frac{7\times 1}{12\times 40}.

$$\frac{7}{480}+\frac{24.5}{50}\times 0.025+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

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

$$\frac{7}{480}+\frac{245}{500}\times 0.025+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

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

$$\frac{7}{480}+\frac{49}{100}\times 0.025+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Me tahuri ki tau ā-ira 0.025 ki te hautau \frac{25}{1000}. Whakahekea te hautanga \frac{25}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\frac{7}{480}+\frac{49}{100}\times \frac{1}{40}+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Me whakarea te \frac{49}{100} ki te \frac{1}{40} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7}{480}+\frac{49\times 1}{100\times 40}+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Mahia ngā whakarea i roto i te hautanga \frac{49\times 1}{100\times 40}.

$$\frac{7}{480}+\frac{49}{4000}+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Ko te maha noa iti rawa atu o 480 me 4000 ko 12000. Me tahuri \frac{7}{480} me \frac{49}{4000} ki te hautau me te tautūnga 12000.

$$\frac{175}{12000}+\frac{147}{12000}+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Tā te mea he rite te tauraro o \frac{175}{12000} me \frac{147}{12000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{175+147}{12000}+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Tāpirihia te 175 ki te 147, ka 322.

$$\frac{322}{12000}+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Whakahekea te hautanga \frac{322}{12000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{161}{6000}+\frac{x}{48+52}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

Tāpirihia te 48 ki te 52, ka 100.

$$\frac{161}{6000}+\frac{x}{100}\times 0.05+\frac{8}{10}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

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

$$\frac{161}{6000}+\frac{x}{100}\times 0.05+\frac{4}{5}\times 0.15+\frac{12}{30}\times 0.75>0.5$$

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.

$$\frac{161}{6000}+\frac{x}{100}\times 0.05+\frac{4}{5}\times \frac{3}{20}+\frac{12}{30}\times 0.75>0.5$$

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

$$\frac{161}{6000}+\frac{x}{100}\times 0.05+\frac{4\times 3}{5\times 20}+\frac{12}{30}\times 0.75>0.5$$

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

$$\frac{161}{6000}+\frac{x}{100}\times 0.05+\frac{12}{100}+\frac{12}{30}\times 0.75>0.5$$

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

$$\frac{161}{6000}+\frac{x}{100}\times 0.05+\frac{3}{25}+\frac{12}{30}\times 0.75>0.5$$

Ko te maha noa iti rawa atu o 6000 me 25 ko 6000. Me tahuri \frac{161}{6000} me \frac{3}{25} ki te hautau me te tautūnga 6000.

$$\frac{161}{6000}+\frac{x}{100}\times 0.05+\frac{720}{6000}+\frac{12}{30}\times 0.75>0.5$$

Tā te mea he rite te tauraro o \frac{161}{6000} me \frac{720}{6000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{161+720}{6000}+\frac{x}{100}\times 0.05+\frac{12}{30}\times 0.75>0.5$$

Tāpirihia te 161 ki te 720, ka 881.

$$\frac{881}{6000}+\frac{x}{100}\times 0.05+\frac{12}{30}\times 0.75>0.5$$

Whakahekea te hautanga \frac{12}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{881}{6000}+\frac{x}{100}\times 0.05+\frac{2}{5}\times 0.75>0.5$$

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.

$$\frac{881}{6000}+\frac{x}{100}\times 0.05+\frac{2}{5}\times \frac{3}{4}>0.5$$

Me whakarea te \frac{2}{5} ki te \frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{881}{6000}+\frac{x}{100}\times 0.05+\frac{2\times 3}{5\times 4}>0.5$$

Mahia ngā whakarea i roto i te hautanga \frac{2\times 3}{5\times 4}.

$$\frac{881}{6000}+\frac{x}{100}\times 0.05+\frac{6}{20}>0.5$$

Whakahekea te hautanga \frac{6}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{881}{6000}+\frac{x}{100}\times 0.05+\frac{3}{10}>0.5$$

Ko te maha noa iti rawa atu o 6000 me 10 ko 6000. Me tahuri \frac{881}{6000} me \frac{3}{10} ki te hautau me te tautūnga 6000.

$$\frac{881}{6000}+\frac{x}{100}\times 0.05+\frac{1800}{6000}>0.5$$

Tā te mea he rite te tauraro o \frac{881}{6000} me \frac{1800}{6000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{881+1800}{6000}+\frac{x}{100}\times 0.05>0.5$$

Tāpirihia te 881 ki te 1800, ka 2681.

$$\frac{2681}{6000}+\frac{x}{100}\times 0.05>0.5$$

Tangohia te \frac{2681}{6000} mai i ngā taha e rua.

$$\frac{x}{100}\times 0.05>0.5-\frac{2681}{6000}$$

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.

$$\frac{x}{100}\times 0.05>\frac{1}{2}-\frac{2681}{6000}$$

Ko te maha noa iti rawa atu o 2 me 6000 ko 6000. Me tahuri \frac{1}{2} me \frac{2681}{6000} ki te hautau me te tautūnga 6000.

$$\frac{x}{100}\times 0.05>\frac{3000}{6000}-\frac{2681}{6000}$$

Tā te mea he rite te tauraro o \frac{3000}{6000} me \frac{2681}{6000}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x}{100}\times 0.05>\frac{3000-2681}{6000}$$

Tangohia te 2681 i te 3000, ka 319.

$$\frac{x}{100}\times 0.05>\frac{319}{6000}$$

Whakawehea ngā taha e rua ki te 0.05. Nō te mea he >0 te 0.05, ka noho pērā tonu te ahunga koreōrite.

$$\frac{x}{100}>\frac{\frac{319}{6000}}{0.05}$$

Tuhia te \frac{\frac{319}{6000}}{0.05} hei hautanga kotahi.

$$\frac{x}{100}>\frac{319}{6000\times 0.05}$$

Whakareatia te 6000 ki te 0.05, ka 300.

$$\frac{x}{100}>\frac{319}{300}$$

Me whakarea ngā taha e rua ki te 100. Nō te mea he >0 te 100, ka noho pērā tonu te ahunga koreōrite.

$$x>\frac{319}{300}\times 100$$

Tuhia te \frac{319}{300}\times 100 hei hautanga kotahi.

$$x>\frac{319\times 100}{300}$$

Whakareatia te 319 ki te 100, ka 31900.

$$x>\frac{31900}{300}$$

Whakahekea te hautanga \frac{31900}{300} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 100.

$$x>\frac{319}{3}$$