Whakaoti i te 2/3(t-2)=3/4(t+2)

$$\frac { 2 } { 3 } ( t - 2 ) = \frac { 3 } { 4 } ( t + 2 )$$

Whakaoti mō t

$$t=-34$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\frac{2}{3}t+\frac{2}{3}\left(-2\right)=\frac{3}{4}\left(t+2\right)$$

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

$$\frac{2}{3}t+\frac{2\left(-2\right)}{3}=\frac{3}{4}\left(t+2\right)$$

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

$$\frac{2}{3}t+\frac{-4}{3}=\frac{3}{4}\left(t+2\right)$$

Ka taea te hautanga \frac{-4}{3} te tuhi anō ko -\frac{4}{3} mā te tango i te tohu tōraro.

$$\frac{2}{3}t-\frac{4}{3}=\frac{3}{4}\left(t+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4} ki te t+2.

$$\frac{2}{3}t-\frac{4}{3}=\frac{3}{4}t+\frac{3}{4}\times 2$$

Tuhia te \frac{3}{4}\times 2 hei hautanga kotahi.

$$\frac{2}{3}t-\frac{4}{3}=\frac{3}{4}t+\frac{3\times 2}{4}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{2}{3}t-\frac{4}{3}=\frac{3}{4}t+\frac{6}{4}$$

Whakahekea te hautanga \frac{6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{2}{3}t-\frac{4}{3}=\frac{3}{4}t+\frac{3}{2}$$

Tangohia te \frac{3}{4}t mai i ngā taha e rua.

$$\frac{2}{3}t-\frac{4}{3}-\frac{3}{4}t=\frac{3}{2}$$

Pahekotia te \frac{2}{3}t me -\frac{3}{4}t, ka -\frac{1}{12}t.

$$-\frac{1}{12}t-\frac{4}{3}=\frac{3}{2}$$

Me tāpiri te \frac{4}{3} ki ngā taha e rua.

$$-\frac{1}{12}t=\frac{3}{2}+\frac{4}{3}$$

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri \frac{3}{2} me \frac{4}{3} ki te hautau me te tautūnga 6.

$$-\frac{1}{12}t=\frac{9}{6}+\frac{8}{6}$$

Tā te mea he rite te tauraro o \frac{9}{6} me \frac{8}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$-\frac{1}{12}t=\frac{9+8}{6}$$

Tāpirihia te 9 ki te 8, ka 17.

$$-\frac{1}{12}t=\frac{17}{6}$$

Me whakarea ngā taha e rua ki te -12, te tau utu o -\frac{1}{12}.

$$t=\frac{17}{6}\left(-12\right)$$

Tuhia te \frac{17}{6}\left(-12\right) hei hautanga kotahi.

$$t=\frac{17\left(-12\right)}{6}$$

Whakareatia te 17 ki te -12, ka -204.

$$t=\frac{-204}{6}$$

Whakawehea te -204 ki te 6, kia riro ko -34.

$$t=-34$$