Whakaoti i te 1/2(x-1)-1/3(x+3)=1/6

$$\frac { 1 } { 2 } ( x - 1 ) - \frac { 1 } { 3 } ( x + 3 ) = \frac { 1 } { 6 }$$

Whakaoti mō x

$$x=10$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\frac{1}{2}x+\frac{1}{2}\left(-1\right)-\frac{1}{3}\left(x+3\right)=\frac{1}{6}$$

Whakareatia te \frac{1}{2} ki te -1, ka -\frac{1}{2}.

$$\frac{1}{2}x-\frac{1}{2}-\frac{1}{3}\left(x+3\right)=\frac{1}{6}$$

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

$$\frac{1}{2}x-\frac{1}{2}-\frac{1}{3}x-\frac{1}{3}\times 3=\frac{1}{6}$$

Me whakakore te 3 me te 3.

$$\frac{1}{2}x-\frac{1}{2}-\frac{1}{3}x-1=\frac{1}{6}$$

Pahekotia te \frac{1}{2}x me -\frac{1}{3}x, ka \frac{1}{6}x.

$$\frac{1}{6}x-\frac{1}{2}-1=\frac{1}{6}$$

Me tahuri te 1 ki te hautau \frac{2}{2}.

$$\frac{1}{6}x-\frac{1}{2}-\frac{2}{2}=\frac{1}{6}$$

Tā te mea he rite te tauraro o -\frac{1}{2} me \frac{2}{2}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{6}x+\frac{-1-2}{2}=\frac{1}{6}$$

Tangohia te 2 i te -1, ka -3.

$$\frac{1}{6}x-\frac{3}{2}=\frac{1}{6}$$

Me tāpiri te \frac{3}{2} ki ngā taha e rua.

$$\frac{1}{6}x=\frac{1}{6}+\frac{3}{2}$$

Ko te maha noa iti rawa atu o 6 me 2 ko 6. Me tahuri \frac{1}{6} me \frac{3}{2} ki te hautau me te tautūnga 6.

$$\frac{1}{6}x=\frac{1}{6}+\frac{9}{6}$$

Tā te mea he rite te tauraro o \frac{1}{6} me \frac{9}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{6}x=\frac{1+9}{6}$$

Tāpirihia te 1 ki te 9, ka 10.

$$\frac{1}{6}x=\frac{10}{6}$$

Whakahekea te hautanga \frac{10}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{6}x=\frac{5}{3}$$

Me whakarea ngā taha e rua ki te 6, te tau utu o \frac{1}{6}.

$$x=\frac{5}{3}\times 6$$

Tuhia te \frac{5}{3}\times 6 hei hautanga kotahi.

$$x=\frac{5\times 6}{3}$$

Whakareatia te 5 ki te 6, ka 30.

$$x=\frac{30}{3}$$

Whakawehea te 30 ki te 3, kia riro ko 10.

$$x=10$$