Whakaoti i te 12(3x/4-x/3)-18(7/9x-5/6x)=x-5

$$12 ( \frac { 3 x } { 4 } - \frac { x } { 3 } ) - 18 ( \frac { 7 } { 9 } x - \frac { 5 } { 6 } x ) = x - 5$$

Whakaoti mō x

$$x=-1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 36, arā, te tauraro pātahi he tino iti rawa te kitea o 4,3,9,6.

$$432\left(\frac{3x}{4}-\frac{x}{3}\right)-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 4 me 3 ko 12. Whakareatia \frac{3x}{4} ki te \frac{3}{3}. Whakareatia \frac{x}{3} ki te \frac{4}{4}.

$$432\left(\frac{3\times 3x}{12}-\frac{4x}{12}\right)-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Tā te mea he rite te tauraro o \frac{3\times 3x}{12} me \frac{4x}{12}, me tango rāua mā te tango i ō raua taurunga.

$$432\times \frac{3\times 3x-4x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Mahia ngā whakarea i roto o 3\times 3x-4x.

$$432\times \frac{9x-4x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Whakakotahitia ngā kupu rite i 9x-4x.

$$432\times \frac{5x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Whakakorea atu te tauwehe pūnoa nui rawa 12 i roto i te 432 me te 12.

$$36\times 5x-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Pahekotia te \frac{7}{9}x me -\frac{5}{6}x, ka -\frac{1}{18}x.

$$36\times 5x-648\left(-\frac{1}{18}\right)x=36x-180$$

Tuhia te 648\left(-\frac{1}{18}\right) hei hautanga kotahi.

$$36\times 5x-\frac{648\left(-1\right)}{18}x=36x-180$$

Whakareatia te 648 ki te -1, ka -648.

$$36\times 5x-\frac{-648}{18}x=36x-180$$

Whakawehea te -648 ki te 18, kia riro ko -36.

$$36\times 5x-\left(-36x\right)=36x-180$$

Ko te tauaro o -36x ko 36x.

$$36\times 5x+36x=36x-180$$

Whakareatia te 36 ki te 5, ka 180.

$$180x+36x=36x-180$$

Pahekotia te 180x me 36x, ka 216x.

$$216x=36x-180$$

Tangohia te 36x mai i ngā taha e rua.

$$216x-36x=-180$$

Pahekotia te 216x me -36x, ka 180x.

$$180x=-180$$

Whakawehea ngā taha e rua ki te 180.

$$x=\frac{-180}{180}$$

Whakawehea te -180 ki te 180, kia riro ko -1.

$$x=-1$$