Whakaoti i te 2/7(t+2/3)=1/5(t-2/3)

$$\frac { 2 } { 7 } ( t + \frac { 2 } { 3 } ) = \frac { 1 } { 5 } ( t - \frac { 2 } { 3 } )$$

Whakaoti mō t

$$t = -\frac{34}{9} = -3\frac{7}{9} \approx -3.777777778$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{2}{7} ki te t+\frac{2}{3}.

$$\frac{2}{7}t+\frac{2}{7}\times \frac{2}{3}=\frac{1}{5}\left(t-\frac{2}{3}\right)$$

Me whakarea te \frac{2}{7} ki te \frac{2}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{2}{7}t+\frac{2\times 2}{7\times 3}=\frac{1}{5}\left(t-\frac{2}{3}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{2\times 2}{7\times 3}.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}\left(t-\frac{2}{3}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{5} ki te t-\frac{2}{3}.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}t+\frac{1}{5}\left(-\frac{2}{3}\right)$$

Me whakarea te \frac{1}{5} ki te -\frac{2}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}t+\frac{1\left(-2\right)}{5\times 3}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\left(-2\right)}{5\times 3}.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}t+\frac{-2}{15}$$

Ka taea te hautanga \frac{-2}{15} te tuhi anō ko -\frac{2}{15} mā te tango i te tohu tōraro.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}t-\frac{2}{15}$$

Tangohia te \frac{1}{5}t mai i ngā taha e rua.

$$\frac{2}{7}t+\frac{4}{21}-\frac{1}{5}t=-\frac{2}{15}$$

Pahekotia te \frac{2}{7}t me -\frac{1}{5}t, ka \frac{3}{35}t.

$$\frac{3}{35}t+\frac{4}{21}=-\frac{2}{15}$$

Tangohia te \frac{4}{21} mai i ngā taha e rua.

$$\frac{3}{35}t=-\frac{2}{15}-\frac{4}{21}$$

Ko te maha noa iti rawa atu o 15 me 21 ko 105. Me tahuri -\frac{2}{15} me \frac{4}{21} ki te hautau me te tautūnga 105.

$$\frac{3}{35}t=-\frac{14}{105}-\frac{20}{105}$$

Tā te mea he rite te tauraro o -\frac{14}{105} me \frac{20}{105}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3}{35}t=\frac{-14-20}{105}$$

Tangohia te 20 i te -14, ka -34.

$$\frac{3}{35}t=-\frac{34}{105}$$

Me whakarea ngā taha e rua ki te \frac{35}{3}, te tau utu o \frac{3}{35}.

$$t=-\frac{34}{105}\times \frac{35}{3}$$

Me whakarea te -\frac{34}{105} ki te \frac{35}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$t=\frac{-34\times 35}{105\times 3}$$

Mahia ngā whakarea i roto i te hautanga \frac{-34\times 35}{105\times 3}.

$$t=\frac{-1190}{315}$$

Whakahekea te hautanga \frac{-1190}{315} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 35.

$$t=-\frac{34}{9}$$