Whakaoti i te 2/3(x-1)=5/6(3-2x)-x

$$\frac { 2 } { 3 } ( x - 1 ) = \frac { 5 } { 6 } ( 3 - 2 x ) - x$$

Whakaoti mō x

$$x=\frac{19}{20}=0.95$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\frac{2}{3}x+\frac{2}{3}\left(-1\right)=\frac{5}{6}\left(3-2x\right)-x$$

Whakareatia te \frac{2}{3} ki te -1, ka -\frac{2}{3}.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{6}\left(3-2x\right)-x$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{5}{6} ki te 3-2x.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{6}\times 3+\frac{5}{6}\left(-2\right)x-x$$

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

$$\frac{2}{3}x-\frac{2}{3}=\frac{5\times 3}{6}+\frac{5}{6}\left(-2\right)x-x$$

Whakareatia te 5 ki te 3, ka 15.

$$\frac{2}{3}x-\frac{2}{3}=\frac{15}{6}+\frac{5}{6}\left(-2\right)x-x$$

Whakahekea te hautanga \frac{15}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}+\frac{5}{6}\left(-2\right)x-x$$

Tuhia te \frac{5}{6}\left(-2\right) hei hautanga kotahi.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}+\frac{5\left(-2\right)}{6}x-x$$

Whakareatia te 5 ki te -2, ka -10.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}+\frac{-10}{6}x-x$$

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

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

Pahekotia te -\frac{5}{3}x me -x, ka -\frac{8}{3}x.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}-\frac{8}{3}x$$

Me tāpiri te \frac{8}{3}x ki ngā taha e rua.

$$\frac{2}{3}x-\frac{2}{3}+\frac{8}{3}x=\frac{5}{2}$$

Pahekotia te \frac{2}{3}x me \frac{8}{3}x, ka \frac{10}{3}x.

$$\frac{10}{3}x-\frac{2}{3}=\frac{5}{2}$$

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

$$\frac{10}{3}x=\frac{5}{2}+\frac{2}{3}$$

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri \frac{5}{2} me \frac{2}{3} ki te hautau me te tautūnga 6.

$$\frac{10}{3}x=\frac{15}{6}+\frac{4}{6}$$

Tā te mea he rite te tauraro o \frac{15}{6} me \frac{4}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{10}{3}x=\frac{15+4}{6}$$

Tāpirihia te 15 ki te 4, ka 19.

$$\frac{10}{3}x=\frac{19}{6}$$

Me whakarea ngā taha e rua ki te \frac{3}{10}, te tau utu o \frac{10}{3}.

$$x=\frac{19}{6}\times \frac{3}{10}$$

Me whakarea te \frac{19}{6} ki te \frac{3}{10} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{19\times 3}{6\times 10}$$

Mahia ngā whakarea i roto i te hautanga \frac{19\times 3}{6\times 10}.

$$x=\frac{57}{60}$$

Whakahekea te hautanga \frac{57}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=\frac{19}{20}$$