Whakaoti i te 3/4left(y+7right)+1/2left(3y-5right)=9/4left(2y-1right)

$$\frac{ 3 }{ 4 } \left( y+7 \right) + \frac{ 1 }{ 2 } \left( 3y-5 \right) = \frac{ 9 }{ 4 } \left( 2y-1 \right)$$

Whakaoti mō y

$$y = \frac{20}{9} = 2\frac{2}{9} \approx 2.222222222$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4} ki te y+7.

$$\frac{3}{4}y+\frac{3}{4}\times 7+\frac{1}{2}\left(3y-5\right)=\frac{9}{4}\left(2y-1\right)$$

Tuhia te \frac{3}{4}\times 7 hei hautanga kotahi.

$$\frac{3}{4}y+\frac{3\times 7}{4}+\frac{1}{2}\left(3y-5\right)=\frac{9}{4}\left(2y-1\right)$$

Whakareatia te 3 ki te 7, ka 21.

$$\frac{3}{4}y+\frac{21}{4}+\frac{1}{2}\left(3y-5\right)=\frac{9}{4}\left(2y-1\right)$$

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

$$\frac{3}{4}y+\frac{21}{4}+\frac{1}{2}\times 3y+\frac{1}{2}\left(-5\right)=\frac{9}{4}\left(2y-1\right)$$

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

$$\frac{3}{4}y+\frac{21}{4}+\frac{3}{2}y+\frac{1}{2}\left(-5\right)=\frac{9}{4}\left(2y-1\right)$$

Whakareatia te \frac{1}{2} ki te -5, ka \frac{-5}{2}.

$$\frac{3}{4}y+\frac{21}{4}+\frac{3}{2}y+\frac{-5}{2}=\frac{9}{4}\left(2y-1\right)$$

Ka taea te hautanga \frac{-5}{2} te tuhi anō ko -\frac{5}{2} mā te tango i te tohu tōraro.

$$\frac{3}{4}y+\frac{21}{4}+\frac{3}{2}y-\frac{5}{2}=\frac{9}{4}\left(2y-1\right)$$

Pahekotia te \frac{3}{4}y me \frac{3}{2}y, ka \frac{9}{4}y.

$$\frac{9}{4}y+\frac{21}{4}-\frac{5}{2}=\frac{9}{4}\left(2y-1\right)$$

Ko te maha noa iti rawa atu o 4 me 2 ko 4. Me tahuri \frac{21}{4} me \frac{5}{2} ki te hautau me te tautūnga 4.

$$\frac{9}{4}y+\frac{21}{4}-\frac{10}{4}=\frac{9}{4}\left(2y-1\right)$$

Tā te mea he rite te tauraro o \frac{21}{4} me \frac{10}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{9}{4}y+\frac{21-10}{4}=\frac{9}{4}\left(2y-1\right)$$

Tangohia te 10 i te 21, ka 11.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{4}\left(2y-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{9}{4} ki te 2y-1.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{4}\times 2y+\frac{9}{4}\left(-1\right)$$

Tuhia te \frac{9}{4}\times 2 hei hautanga kotahi.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9\times 2}{4}y+\frac{9}{4}\left(-1\right)$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{9}{4}y+\frac{11}{4}=\frac{18}{4}y+\frac{9}{4}\left(-1\right)$$

Whakahekea te hautanga \frac{18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{2}y+\frac{9}{4}\left(-1\right)$$

Whakareatia te \frac{9}{4} ki te -1, ka -\frac{9}{4}.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{2}y-\frac{9}{4}$$

Tangohia te \frac{9}{2}y mai i ngā taha e rua.

$$\frac{9}{4}y+\frac{11}{4}-\frac{9}{2}y=-\frac{9}{4}$$

Pahekotia te \frac{9}{4}y me -\frac{9}{2}y, ka -\frac{9}{4}y.

$$-\frac{9}{4}y+\frac{11}{4}=-\frac{9}{4}$$

Tangohia te \frac{11}{4} mai i ngā taha e rua.

$$-\frac{9}{4}y=-\frac{9}{4}-\frac{11}{4}$$

Tā te mea he rite te tauraro o -\frac{9}{4} me \frac{11}{4}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{9}{4}y=\frac{-9-11}{4}$$

Tangohia te 11 i te -9, ka -20.

$$-\frac{9}{4}y=\frac{-20}{4}$$

Whakawehea te -20 ki te 4, kia riro ko -5.

$$-\frac{9}{4}y=-5$$

Me whakarea ngā taha e rua ki te -\frac{4}{9}, te tau utu o -\frac{9}{4}.

$$y=-5\left(-\frac{4}{9}\right)$$

Tuhia te -5\left(-\frac{4}{9}\right) hei hautanga kotahi.

$$y=\frac{-5\left(-4\right)}{9}$$

Whakareatia te -5 ki te -4, ka 20.

$$y=\frac{20}{9}$$