Whakaoti i te x-1/3left(x-1/3left(x-9right)right)=1/9left(x-9right)

$$x- \frac{ 1 }{ 3 } \left( x- \frac{ 1 }{ 3 } \left( x-9 \right) \right) = \frac{ 1 }{ 9 } \left( x-9 \right)$$

Whakaoti mō x

$$x=0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{3} ki te x-9.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x-\frac{1}{3}\left(-9\right)\right)=\frac{1}{9}\left(x-9\right)$$

Tuhia te -\frac{1}{3}\left(-9\right) hei hautanga kotahi.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+\frac{-\left(-9\right)}{3}\right)=\frac{1}{9}\left(x-9\right)$$

Whakareatia te -1 ki te -9, ka 9.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+\frac{9}{3}\right)=\frac{1}{9}\left(x-9\right)$$

Whakawehea te 9 ki te 3, kia riro ko 3.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+3\right)=\frac{1}{9}\left(x-9\right)$$

Pahekotia te x me -\frac{1}{3}x, ka \frac{2}{3}x.

$$x-\frac{1}{3}\left(\frac{2}{3}x+3\right)=\frac{1}{9}\left(x-9\right)$$

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

$$x-\frac{1}{3}\times \frac{2}{3}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-9\right)$$

Me whakarea te -\frac{1}{3} ki te \frac{2}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x+\frac{-2}{3\times 3}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-9\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{-2}{3\times 3}.

$$x+\frac{-2}{9}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-9\right)$$

Ka taea te hautanga \frac{-2}{9} te tuhi anō ko -\frac{2}{9} mā te tango i te tohu tōraro.

$$x-\frac{2}{9}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-9\right)$$

Me whakakore te 3 me te 3.

$$x-\frac{2}{9}x-1=\frac{1}{9}\left(x-9\right)$$

Pahekotia te x me -\frac{2}{9}x, ka \frac{7}{9}x.

$$\frac{7}{9}x-1=\frac{1}{9}\left(x-9\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{9} ki te x-9.

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{1}{9}\left(-9\right)$$

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

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{-9}{9}$$

Whakawehea te -9 ki te 9, kia riro ko -1.

$$\frac{7}{9}x-1=\frac{1}{9}x-1$$

Tangohia te \frac{1}{9}x mai i ngā taha e rua.

$$\frac{7}{9}x-1-\frac{1}{9}x=-1$$

Pahekotia te \frac{7}{9}x me -\frac{1}{9}x, ka \frac{2}{3}x.

$$\frac{2}{3}x-1=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$\frac{2}{3}x=-1+1$$

Tāpirihia te -1 ki te 1, ka 0.

$$\frac{2}{3}x=0$$

He ōrite te hua o ngā tau e rua ki 0 ina 0 tētahi o rāua te iti rawa. Tātemea kāore te \frac{2}{3} e ōrite ki 0, me ōrite pū te x ki 0.

$$x=0$$