Whakaoti i te x-1/3[x-1/3(x-9)]=1/9(x-4)

$$x - \frac { 1 } { 3 } [ x - \frac { 1 } { 3 } ( x - 9 ) ] = \frac { 1 } { 9 } ( x - 4 )$$

Whakaoti mō x

$$x=\frac{5}{6}\approx 0.833333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x-\frac{1}{3}\left(x-\frac{1}{3}x-\frac{1}{3}\left(-9\right)\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+\frac{-\left(-9\right)}{3}\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+\frac{9}{3}\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+3\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\left(\frac{2}{3}x+3\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\times \frac{2}{3}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

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

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

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

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

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

$$x-\frac{2}{9}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

Me whakakore te 3 me te 3.

$$x-\frac{2}{9}x-1=\frac{1}{9}\left(x-4\right)$$

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

$$\frac{7}{9}x-1=\frac{1}{9}\left(x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{9} ki te x-4.

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{1}{9}\left(-4\right)$$

Whakareatia te \frac{1}{9} ki te -4, ka \frac{-4}{9}.

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{-4}{9}$$

Ka taea te hautanga \frac{-4}{9} te tuhi anō ko -\frac{4}{9} mā te tango i te tohu tōraro.

$$\frac{7}{9}x-1=\frac{1}{9}x-\frac{4}{9}$$

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

$$\frac{7}{9}x-1-\frac{1}{9}x=-\frac{4}{9}$$

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

$$\frac{2}{3}x-1=-\frac{4}{9}$$

Me tāpiri te 1 ki ngā taha e rua.

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

Me tahuri te 1 ki te hautau \frac{9}{9}.

$$\frac{2}{3}x=-\frac{4}{9}+\frac{9}{9}$$

Tā te mea he rite te tauraro o -\frac{4}{9} me \frac{9}{9}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2}{3}x=\frac{-4+9}{9}$$

Tāpirihia te -4 ki te 9, ka 5.

$$\frac{2}{3}x=\frac{5}{9}$$

Me whakarea ngā taha e rua ki te \frac{3}{2}, te tau utu o \frac{2}{3}.

$$x=\frac{5}{9}\times \frac{3}{2}$$

Me whakarea te \frac{5}{9} ki te \frac{3}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{5\times 3}{9\times 2}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\times 3}{9\times 2}.

$$x=\frac{15}{18}$$

Whakahekea te hautanga \frac{15}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=\frac{5}{6}$$