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

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

Whakaoti mō x

$$x>-\frac{213}{5}$$

Ngā Upane Otinga

Tāpirihia te 28 ki te 24.5, ka 52.5.

$$\frac{52.5+x}{48+50+48+52}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

Tāpirihia te 48 ki te 50, ka 98.

$$\frac{52.5+x}{98+48+52}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

Tāpirihia te 98 ki te 48, ka 146.

$$\frac{52.5+x}{146+52}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

Tāpirihia te 146 ki te 52, ka 198.

$$\frac{52.5+x}{198}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

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

$$\frac{52.5+x}{198}\times 0.1+\frac{4}{5}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

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.

$$\frac{52.5+x}{198}\times 0.1+\frac{4}{5}\times \frac{3}{20}+\frac{15}{30}\times 0.75>0.5$$

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

$$\frac{52.5+x}{198}\times 0.1+\frac{4\times 3}{5\times 20}+\frac{15}{30}\times 0.75>0.5$$

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

$$\frac{52.5+x}{198}\times 0.1+\frac{12}{100}+\frac{15}{30}\times 0.75>0.5$$

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

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{15}{30}\times 0.75>0.5$$

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

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{1}{2}\times 0.75>0.5$$

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.

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{1}{2}\times \frac{3}{4}>0.5$$

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

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{1\times 3}{2\times 4}>0.5$$

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

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{3}{8}>0.5$$

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.

$$\frac{52.5+x}{198}\times 0.1+\frac{24}{200}+\frac{75}{200}>0.5$$

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.

$$\frac{52.5+x}{198}\times 0.1+\frac{24+75}{200}>0.5$$

Tāpirihia te 24 ki te 75, ka 99.

$$\frac{52.5+x}{198}\times 0.1+\frac{99}{200}>0.5$$

Whakawehea ia wā o 52.5+x ki te 198, kia riro ko \frac{35}{132}+\frac{1}{198}x.

$$\left(\frac{35}{132}+\frac{1}{198}x\right)\times 0.1+\frac{99}{200}>0.5$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{35}{132}+\frac{1}{198}x ki te 0.1.

$$\frac{7}{264}+\frac{1}{198}x\times 0.1+\frac{99}{200}>0.5$$

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

$$\frac{7}{264}+\frac{1}{198}x\times \frac{1}{10}+\frac{99}{200}>0.5$$

Me whakarea te \frac{1}{198} ki te \frac{1}{10} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7}{264}+\frac{1\times 1}{198\times 10}x+\frac{99}{200}>0.5$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 1}{198\times 10}.

$$\frac{7}{264}+\frac{1}{1980}x+\frac{99}{200}>0.5$$

Ko te maha noa iti rawa atu o 264 me 200 ko 6600. Me tahuri \frac{7}{264} me \frac{99}{200} ki te hautau me te tautūnga 6600.

$$\frac{175}{6600}+\frac{1}{1980}x+\frac{3267}{6600}>0.5$$

Tā te mea he rite te tauraro o \frac{175}{6600} me \frac{3267}{6600}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{175+3267}{6600}+\frac{1}{1980}x>0.5$$

Tāpirihia te 175 ki te 3267, ka 3442.

$$\frac{3442}{6600}+\frac{1}{1980}x>0.5$$

Whakahekea te hautanga \frac{3442}{6600} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1721}{3300}+\frac{1}{1980}x>0.5$$

Tangohia te \frac{1721}{3300} mai i ngā taha e rua.

$$\frac{1}{1980}x>0.5-\frac{1721}{3300}$$

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.

$$\frac{1}{1980}x>\frac{1}{2}-\frac{1721}{3300}$$

Ko te maha noa iti rawa atu o 2 me 3300 ko 3300. Me tahuri \frac{1}{2} me \frac{1721}{3300} ki te hautau me te tautūnga 3300.

$$\frac{1}{1980}x>\frac{1650}{3300}-\frac{1721}{3300}$$

Tā te mea he rite te tauraro o \frac{1650}{3300} me \frac{1721}{3300}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{1980}x>\frac{1650-1721}{3300}$$

Tangohia te 1721 i te 1650, ka -71.

$$\frac{1}{1980}x>-\frac{71}{3300}$$

Me whakarea ngā taha e rua ki te 1980, te tau utu o \frac{1}{1980}. Nō te mea he >0 te \frac{1}{1980}, ka noho pērā tonu te ahunga koreōrite.

$$x>-\frac{71}{3300}\times 1980$$

Tuhia te -\frac{71}{3300}\times 1980 hei hautanga kotahi.

$$x>\frac{-71\times 1980}{3300}$$

Whakareatia te -71 ki te 1980, ka -140580.

$$x>\frac{-140580}{3300}$$

Whakahekea te hautanga \frac{-140580}{3300} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 660.

$$x>-\frac{213}{5}$$