Whakaoti i te 3/7=3/2-1/3+3/7x

$$\frac { 3 } { 7 } = \frac { 3 } { 2 } - \frac { 1 } { 3 } + \frac { 3 } { 7 } x$$

Whakaoti mō x

$$x = -\frac{31}{18} = -1\frac{13}{18} \approx -1.722222222$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri \frac{3}{2} me \frac{1}{3} ki te hautau me te tautūnga 6.

$$\frac{3}{7}=\frac{9}{6}-\frac{2}{6}+\frac{3}{7}x$$

Tā te mea he rite te tauraro o \frac{9}{6} me \frac{2}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3}{7}=\frac{9-2}{6}+\frac{3}{7}x$$

Tangohia te 2 i te 9, ka 7.

$$\frac{3}{7}=\frac{7}{6}+\frac{3}{7}x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{7}{6}+\frac{3}{7}x=\frac{3}{7}$$

Tangohia te \frac{7}{6} mai i ngā taha e rua.

$$\frac{3}{7}x=\frac{3}{7}-\frac{7}{6}$$

Ko te maha noa iti rawa atu o 7 me 6 ko 42. Me tahuri \frac{3}{7} me \frac{7}{6} ki te hautau me te tautūnga 42.

$$\frac{3}{7}x=\frac{18}{42}-\frac{49}{42}$$

Tā te mea he rite te tauraro o \frac{18}{42} me \frac{49}{42}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3}{7}x=\frac{18-49}{42}$$

Tangohia te 49 i te 18, ka -31.

$$\frac{3}{7}x=-\frac{31}{42}$$

Me whakarea ngā taha e rua ki te \frac{7}{3}, te tau utu o \frac{3}{7}.

$$x=-\frac{31}{42}\times \frac{7}{3}$$

Me whakarea te -\frac{31}{42} ki te \frac{7}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-31\times 7}{42\times 3}$$

Mahia ngā whakarea i roto i te hautanga \frac{-31\times 7}{42\times 3}.

$$x=\frac{-217}{126}$$

Whakahekea te hautanga \frac{-217}{126} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$x=-\frac{31}{18}$$