Whakaoti i te -31/5x+71/10=42/9

$$-3 \frac{ 1 }{ 5 } x+7 \frac{ 1 }{ 10 } = 4 \frac{ 2 }{ 9 }$$

Whakaoti mō x

$$x=\frac{259}{288}\approx 0.899305556$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 90, arā, te tauraro pātahi he tino iti rawa te kitea o 5,10,9.

$$90\left(-\frac{3\times 5+1}{5}\right)x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Whakareatia te 3 ki te 5, ka 15.

$$90\left(-\frac{15+1}{5}\right)x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Tāpirihia te 15 ki te 1, ka 16.

$$90\left(-\frac{16}{5}\right)x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Tuhia te 90\left(-\frac{16}{5}\right) hei hautanga kotahi.

$$\frac{90\left(-16\right)}{5}x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Whakareatia te 90 ki te -16, ka -1440.

$$\frac{-1440}{5}x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Whakawehea te -1440 ki te 5, kia riro ko -288.

$$-288x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Whakareatia te 7 ki te 10, ka 70.

$$-288x+9\left(70+1\right)=10\left(4\times 9+2\right)$$

Tāpirihia te 70 ki te 1, ka 71.

$$-288x+9\times 71=10\left(4\times 9+2\right)$$

Whakareatia te 9 ki te 71, ka 639.

$$-288x+639=10\left(4\times 9+2\right)$$

Whakareatia te 4 ki te 9, ka 36.

$$-288x+639=10\left(36+2\right)$$

Tāpirihia te 36 ki te 2, ka 38.

$$-288x+639=10\times 38$$

Whakareatia te 10 ki te 38, ka 380.

$$-288x+639=380$$

Tangohia te 639 mai i ngā taha e rua.

$$-288x=380-639$$

Tangohia te 639 i te 380, ka -259.

$$-288x=-259$$

Whakawehea ngā taha e rua ki te -288.

$$x=\frac{-259}{-288}$$

Ka taea te hautanga \frac{-259}{-288} te whakamāmā ki te \frac{259}{288} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{259}{288}$$