Whakaoti i te (3/7x-5/6)*12/13=21/2

$$( \frac{ 3 }{ 7 } x- \frac{ 5 }{ 6 } ) \times 1 \frac{ 2 }{ 13 } =2 \frac{ 1 }{ 2 }$$

Whakaoti mō x

$$x=7$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 546, arā, te tauraro pātahi he tino iti rawa te kitea o 7,6,13,2.

$$42\left(\frac{3}{7}x-\frac{5}{6}\right)\left(1\times 13+2\right)=273\left(2\times 2+1\right)$$

Whakareatia te 1 ki te 13, ka 13.

$$42\left(\frac{3}{7}x-\frac{5}{6}\right)\left(13+2\right)=273\left(2\times 2+1\right)$$

Tāpirihia te 13 ki te 2, ka 15.

$$42\left(\frac{3}{7}x-\frac{5}{6}\right)\times 15=273\left(2\times 2+1\right)$$

Whakareatia te 42 ki te 15, ka 630.

$$630\left(\frac{3}{7}x-\frac{5}{6}\right)=273\left(2\times 2+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 630 ki te \frac{3}{7}x-\frac{5}{6}.

$$630\times \frac{3}{7}x+630\left(-\frac{5}{6}\right)=273\left(2\times 2+1\right)$$

Tuhia te 630\times \frac{3}{7} hei hautanga kotahi.

$$\frac{630\times 3}{7}x+630\left(-\frac{5}{6}\right)=273\left(2\times 2+1\right)$$

Whakareatia te 630 ki te 3, ka 1890.

$$\frac{1890}{7}x+630\left(-\frac{5}{6}\right)=273\left(2\times 2+1\right)$$

Whakawehea te 1890 ki te 7, kia riro ko 270.

$$270x+630\left(-\frac{5}{6}\right)=273\left(2\times 2+1\right)$$

Tuhia te 630\left(-\frac{5}{6}\right) hei hautanga kotahi.

$$270x+\frac{630\left(-5\right)}{6}=273\left(2\times 2+1\right)$$

Whakareatia te 630 ki te -5, ka -3150.

$$270x+\frac{-3150}{6}=273\left(2\times 2+1\right)$$

Whakawehea te -3150 ki te 6, kia riro ko -525.

$$270x-525=273\left(2\times 2+1\right)$$

Whakareatia te 2 ki te 2, ka 4.

$$270x-525=273\left(4+1\right)$$

Tāpirihia te 4 ki te 1, ka 5.

$$270x-525=273\times 5$$

Whakareatia te 273 ki te 5, ka 1365.

$$270x-525=1365$$

Me tāpiri te 525 ki ngā taha e rua.

$$270x=1365+525$$

Tāpirihia te 1365 ki te 525, ka 1890.

$$270x=1890$$

Whakawehea ngā taha e rua ki te 270.

$$x=\frac{1890}{270}$$

Whakawehea te 1890 ki te 270, kia riro ko 7.

$$x=7$$