Whakaoti i te 10-x/10-30=-5-50/-5-25

$$\frac{ 10-x }{ 10-30 } = \frac{ -5-50 }{ -5-25 }$$

Whakaoti mō x

$$x = \frac{140}{3} = 46\frac{2}{3} \approx 46.666666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 30 i te 10, ka -20.

$$\frac{10-x}{-20}=\frac{-5-50}{-5-25}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-10+x}{20}=\frac{-5-50}{-5-25}$$

Tangohia te 50 i te -5, ka -55.

$$\frac{-10+x}{20}=\frac{-55}{-5-25}$$

Tangohia te 25 i te -5, ka -30.

$$\frac{-10+x}{20}=\frac{-55}{-30}$$

Whakahekea te hautanga \frac{-55}{-30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -5.

$$\frac{-10+x}{20}=\frac{11}{6}$$

Whakawehea ia wā o -10+x ki te 20, kia riro ko -\frac{1}{2}+\frac{1}{20}x.

$$-\frac{1}{2}+\frac{1}{20}x=\frac{11}{6}$$

Me tāpiri te \frac{1}{2} ki ngā taha e rua.

$$\frac{1}{20}x=\frac{11}{6}+\frac{1}{2}$$

Ko te maha noa iti rawa atu o 6 me 2 ko 6. Me tahuri \frac{11}{6} me \frac{1}{2} ki te hautau me te tautūnga 6.

$$\frac{1}{20}x=\frac{11}{6}+\frac{3}{6}$$

Tā te mea he rite te tauraro o \frac{11}{6} me \frac{3}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{20}x=\frac{11+3}{6}$$

Tāpirihia te 11 ki te 3, ka 14.

$$\frac{1}{20}x=\frac{14}{6}$$

Whakahekea te hautanga \frac{14}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{20}x=\frac{7}{3}$$

Me whakarea ngā taha e rua ki te 20, te tau utu o \frac{1}{20}.

$$x=\frac{7}{3}\times 20$$

Tuhia te \frac{7}{3}\times 20 hei hautanga kotahi.

$$x=\frac{7\times 20}{3}$$

Whakareatia te 7 ki te 20, ka 140.

$$x=\frac{140}{3}$$