Whakaoti i te 1/3(2y+1)+1/2y=2/5(1-2y)-4

$$\frac { 1 } { 3 } ( 2 y + 1 ) + \frac { 1 } { 2 } y = \frac { 2 } { 5 } ( 1 - 2 y ) - 4$$

Whakaoti mō y

$$y=-2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{3} ki te 2y+1.

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

Whakareatia te \frac{1}{3} ki te 2, ka \frac{2}{3}.

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

Pahekotia te \frac{2}{3}y me \frac{1}{2}y, ka \frac{7}{6}y.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}\left(1-2y\right)-4$$

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

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{2}{5}\left(-2\right)y-4$$

Tuhia te \frac{2}{5}\left(-2\right) hei hautanga kotahi.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{2\left(-2\right)}{5}y-4$$

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

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{-4}{5}y-4$$

Ka taea te hautanga \frac{-4}{5} te tuhi anō ko -\frac{4}{5} mā te tango i te tohu tōraro.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}-\frac{4}{5}y-4$$

Me tahuri te 4 ki te hautau \frac{20}{5}.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}-\frac{4}{5}y-\frac{20}{5}$$

Tā te mea he rite te tauraro o \frac{2}{5} me \frac{20}{5}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2-20}{5}-\frac{4}{5}y$$

Tangohia te 20 i te 2, ka -18.

$$\frac{7}{6}y+\frac{1}{3}=-\frac{18}{5}-\frac{4}{5}y$$

Me tāpiri te \frac{4}{5}y ki ngā taha e rua.

$$\frac{7}{6}y+\frac{1}{3}+\frac{4}{5}y=-\frac{18}{5}$$

Pahekotia te \frac{7}{6}y me \frac{4}{5}y, ka \frac{59}{30}y.

$$\frac{59}{30}y+\frac{1}{3}=-\frac{18}{5}$$

Tangohia te \frac{1}{3} mai i ngā taha e rua.

$$\frac{59}{30}y=-\frac{18}{5}-\frac{1}{3}$$

Ko te maha noa iti rawa atu o 5 me 3 ko 15. Me tahuri -\frac{18}{5} me \frac{1}{3} ki te hautau me te tautūnga 15.

$$\frac{59}{30}y=-\frac{54}{15}-\frac{5}{15}$$

Tā te mea he rite te tauraro o -\frac{54}{15} me \frac{5}{15}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{59}{30}y=\frac{-54-5}{15}$$

Tangohia te 5 i te -54, ka -59.

$$\frac{59}{30}y=-\frac{59}{15}$$

Me whakarea ngā taha e rua ki te \frac{30}{59}, te tau utu o \frac{59}{30}.

$$y=-\frac{59}{15}\times \frac{30}{59}$$

Me whakarea te -\frac{59}{15} ki te \frac{30}{59} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$y=\frac{-59\times 30}{15\times 59}$$

Mahia ngā whakarea i roto i te hautanga \frac{-59\times 30}{15\times 59}.

$$y=\frac{-1770}{885}$$

Whakawehea te -1770 ki te 885, kia riro ko -2.

$$y=-2$$