Whakaoti i te 2/3(x-4)=-7/12(x+6)

$$\frac{ 2 }{ 3 } (x-4)=- \frac{ 7 }{ 12 } (x+6)$$

Whakaoti mō x

$$x=-\frac{2}{3}\approx -0.666666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{2}{3} ki te x-4.

$$\frac{2}{3}x+\frac{2}{3}\left(-4\right)=-\frac{7}{12}\left(x+6\right)$$

Tuhia te \frac{2}{3}\left(-4\right) hei hautanga kotahi.

$$\frac{2}{3}x+\frac{2\left(-4\right)}{3}=-\frac{7}{12}\left(x+6\right)$$

Whakareatia te 2 ki te -4, ka -8.

$$\frac{2}{3}x+\frac{-8}{3}=-\frac{7}{12}\left(x+6\right)$$

Ka taea te hautanga \frac{-8}{3} te tuhi anō ko -\frac{8}{3} mā te tango i te tohu tōraro.

$$\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{7}{12} ki te x+6.

$$\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x-\frac{7}{12}\times 6$$

Tuhia te -\frac{7}{12}\times 6 hei hautanga kotahi.

$$\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x+\frac{-7\times 6}{12}$$

Whakareatia te -7 ki te 6, ka -42.

$$\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x+\frac{-42}{12}$$

Whakahekea te hautanga \frac{-42}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x-\frac{7}{2}$$

Me tāpiri te \frac{7}{12}x ki ngā taha e rua.

$$\frac{2}{3}x-\frac{8}{3}+\frac{7}{12}x=-\frac{7}{2}$$

Pahekotia te \frac{2}{3}x me \frac{7}{12}x, ka \frac{5}{4}x.

$$\frac{5}{4}x-\frac{8}{3}=-\frac{7}{2}$$

Me tāpiri te \frac{8}{3} ki ngā taha e rua.

$$\frac{5}{4}x=-\frac{7}{2}+\frac{8}{3}$$

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri -\frac{7}{2} me \frac{8}{3} ki te hautau me te tautūnga 6.

$$\frac{5}{4}x=-\frac{21}{6}+\frac{16}{6}$$

Tā te mea he rite te tauraro o -\frac{21}{6} me \frac{16}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5}{4}x=\frac{-21+16}{6}$$

Tāpirihia te -21 ki te 16, ka -5.

$$\frac{5}{4}x=-\frac{5}{6}$$

Me whakarea ngā taha e rua ki te \frac{4}{5}, te tau utu o \frac{5}{4}.

$$x=-\frac{5}{6}\times \frac{4}{5}$$

Me whakarea te -\frac{5}{6} ki te \frac{4}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-5\times 4}{6\times 5}$$

Mahia ngā whakarea i roto i te hautanga \frac{-5\times 4}{6\times 5}.

$$x=\frac{-20}{30}$$

Whakahekea te hautanga \frac{-20}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$x=-\frac{2}{3}$$