Whakaoti i te 3/5x-[7/4(x/5+1/2)]=frac{7}{3}y-frac{5}{4}

$$\frac { 3 } { 5 } x - [ \frac { 7 } { 4 } ( \frac { x } { 5 } + \frac { 1 } { 2 } ) ] = \frac { 7 } { 3 } y - \frac { 5 } { 4 }$$

Whakaoti mō x

$$x=\frac{28y}{3}-\frac{3}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 60, arā, te tauraro pātahi he tino iti rawa te kitea o 5,4,2,3.

$$36x-105\left(\frac{x}{5}+\frac{1}{2}\right)=140y-75$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 5 me 2 ko 10. Whakareatia \frac{x}{5} ki te \frac{2}{2}. Whakareatia \frac{1}{2} ki te \frac{5}{5}.

$$36x-105\left(\frac{2x}{10}+\frac{5}{10}\right)=140y-75$$

Tā te mea he rite te tauraro o \frac{2x}{10} me \frac{5}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$36x-105\times \frac{2x+5}{10}=140y-75$$

Tuhia te 105\times \frac{2x+5}{10} hei hautanga kotahi.

$$36x-\frac{105\left(2x+5\right)}{10}=140y-75$$

Whakamahia te āhuatanga tohatoha hei whakarea te 105 ki te 2x+5.

$$36x-\frac{210x+525}{10}=140y-75$$

Whakawehea ia wā o 210x+525 ki te 10, kia riro ko 21x+\frac{105}{2}.

$$36x-\left(21x+\frac{105}{2}\right)=140y-75$$

Hei kimi i te tauaro o 21x+\frac{105}{2}, kimihia te tauaro o ia taurangi.

$$36x-21x-\frac{105}{2}=140y-75$$

Pahekotia te 36x me -21x, ka 15x.

$$15x-\frac{105}{2}=140y-75$$

Me tāpiri te \frac{105}{2} ki ngā taha e rua.

$$15x=140y-75+\frac{105}{2}$$

Tāpirihia te -75 ki te \frac{105}{2}, ka -\frac{45}{2}.

$$15x=140y-\frac{45}{2}$$

Whakawehea ngā taha e rua ki te 15.

$$\frac{15x}{15}=\frac{140y-\frac{45}{2}}{15}$$

Mā te whakawehe ki te 15 ka wetekia te whakareanga ki te 15.

$$x=\frac{140y-\frac{45}{2}}{15}$$

Whakawehe 140y-\frac{45}{2} ki te 15.

$$x=\frac{28y}{3}-\frac{3}{2}$$

Whakaoti mō y

$$y=\frac{3x}{28}+\frac{9}{56}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 60, arā, te tauraro pātahi he tino iti rawa te kitea o 5,4,2,3.

$$36x-105\left(\frac{x}{5}+\frac{1}{2}\right)=140y-75$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 5 me 2 ko 10. Whakareatia \frac{x}{5} ki te \frac{2}{2}. Whakareatia \frac{1}{2} ki te \frac{5}{5}.

$$36x-105\left(\frac{2x}{10}+\frac{5}{10}\right)=140y-75$$

Tā te mea he rite te tauraro o \frac{2x}{10} me \frac{5}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$36x-105\times \frac{2x+5}{10}=140y-75$$

Tuhia te 105\times \frac{2x+5}{10} hei hautanga kotahi.

$$36x-\frac{105\left(2x+5\right)}{10}=140y-75$$

Whakamahia te āhuatanga tohatoha hei whakarea te 105 ki te 2x+5.

$$36x-\frac{210x+525}{10}=140y-75$$

Whakawehea ia wā o 210x+525 ki te 10, kia riro ko 21x+\frac{105}{2}.

$$36x-\left(21x+\frac{105}{2}\right)=140y-75$$

Hei kimi i te tauaro o 21x+\frac{105}{2}, kimihia te tauaro o ia taurangi.

$$36x-21x-\frac{105}{2}=140y-75$$

Pahekotia te 36x me -21x, ka 15x.

$$15x-\frac{105}{2}=140y-75$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$140y-75=15x-\frac{105}{2}$$

Me tāpiri te 75 ki ngā taha e rua.

$$140y=15x-\frac{105}{2}+75$$

Tāpirihia te -\frac{105}{2} ki te 75, ka \frac{45}{2}.

$$140y=15x+\frac{45}{2}$$

Whakawehea ngā taha e rua ki te 140.

$$\frac{140y}{140}=\frac{15x+\frac{45}{2}}{140}$$

Mā te whakawehe ki te 140 ka wetekia te whakareanga ki te 140.

$$y=\frac{15x+\frac{45}{2}}{140}$$

Whakawehe 15x+\frac{45}{2} ki te 140.

$$y=\frac{3x}{28}+\frac{9}{56}$$