Whakaoti i te 1/2(x-1)=2-1/5(x+2)

$$\frac { 1 } { 2 } ( x - 1 ) = 2 - \frac { 1 } { 5 } ( x + 2 )$$

Whakaoti mō x

$$x=3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\frac{1}{2}x+\frac{1}{2}\left(-1\right)=2-\frac{1}{5}\left(x+2\right)$$

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

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}\left(x+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{5} ki te x+2.

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}x-\frac{1}{5}\times 2$$

Tuhia te -\frac{1}{5}\times 2 hei hautanga kotahi.

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}x+\frac{-2}{5}$$

Ka taea te hautanga \frac{-2}{5} te tuhi anō ko -\frac{2}{5} mā te tango i te tohu tōraro.

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}x-\frac{2}{5}$$

Me tahuri te 2 ki te hautau \frac{10}{5}.

$$\frac{1}{2}x-\frac{1}{2}=\frac{10}{5}-\frac{1}{5}x-\frac{2}{5}$$

Tā te mea he rite te tauraro o \frac{10}{5} me \frac{2}{5}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{2}x-\frac{1}{2}=\frac{10-2}{5}-\frac{1}{5}x$$

Tangohia te 2 i te 10, ka 8.

$$\frac{1}{2}x-\frac{1}{2}=\frac{8}{5}-\frac{1}{5}x$$

Me tāpiri te \frac{1}{5}x ki ngā taha e rua.

$$\frac{1}{2}x-\frac{1}{2}+\frac{1}{5}x=\frac{8}{5}$$

Pahekotia te \frac{1}{2}x me \frac{1}{5}x, ka \frac{7}{10}x.

$$\frac{7}{10}x-\frac{1}{2}=\frac{8}{5}$$

Me tāpiri te \frac{1}{2} ki ngā taha e rua.

$$\frac{7}{10}x=\frac{8}{5}+\frac{1}{2}$$

Ko te maha noa iti rawa atu o 5 me 2 ko 10. Me tahuri \frac{8}{5} me \frac{1}{2} ki te hautau me te tautūnga 10.

$$\frac{7}{10}x=\frac{16}{10}+\frac{5}{10}$$

Tā te mea he rite te tauraro o \frac{16}{10} me \frac{5}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7}{10}x=\frac{16+5}{10}$$

Tāpirihia te 16 ki te 5, ka 21.

$$\frac{7}{10}x=\frac{21}{10}$$

Me whakarea ngā taha e rua ki te \frac{10}{7}, te tau utu o \frac{7}{10}.

$$x=\frac{21}{10}\times \frac{10}{7}$$

Me whakarea te \frac{21}{10} ki te \frac{10}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{21\times 10}{10\times 7}$$

Me whakakore tahi te 10 i te taurunga me te tauraro.

$$x=\frac{21}{7}$$

Whakawehea te 21 ki te 7, kia riro ko 3.

$$x=3$$