Whakaoti i te 1-1/6*(2z-5)=1/4*(3-z)

$$1 - \frac { 1 } { 6 } \cdot ( 2 z - 5 ) = \frac { 1 } { 4 } \cdot ( 3 - z )$$

Whakaoti mō z

$$z=13$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{6} ki te 2z-5.

$$1-\frac{1}{6}\times 2z-\frac{1}{6}\left(-5\right)=\frac{1}{4}\left(3-z\right)$$

Tuhia te -\frac{1}{6}\times 2 hei hautanga kotahi.

$$1+\frac{-2}{6}z-\frac{1}{6}\left(-5\right)=\frac{1}{4}\left(3-z\right)$$

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

$$1-\frac{1}{3}z-\frac{1}{6}\left(-5\right)=\frac{1}{4}\left(3-z\right)$$

Tuhia te -\frac{1}{6}\left(-5\right) hei hautanga kotahi.

$$1-\frac{1}{3}z+\frac{-\left(-5\right)}{6}=\frac{1}{4}\left(3-z\right)$$

Whakareatia te -1 ki te -5, ka 5.

$$1-\frac{1}{3}z+\frac{5}{6}=\frac{1}{4}\left(3-z\right)$$

Me tahuri te 1 ki te hautau \frac{6}{6}.

$$\frac{6}{6}-\frac{1}{3}z+\frac{5}{6}=\frac{1}{4}\left(3-z\right)$$

Tā te mea he rite te tauraro o \frac{6}{6} me \frac{5}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{6+5}{6}-\frac{1}{3}z=\frac{1}{4}\left(3-z\right)$$

Tāpirihia te 6 ki te 5, ka 11.

$$\frac{11}{6}-\frac{1}{3}z=\frac{1}{4}\left(3-z\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te 3-z.

$$\frac{11}{6}-\frac{1}{3}z=\frac{1}{4}\times 3+\frac{1}{4}\left(-1\right)z$$

Whakareatia te \frac{1}{4} ki te 3, ka \frac{3}{4}.

$$\frac{11}{6}-\frac{1}{3}z=\frac{3}{4}+\frac{1}{4}\left(-1\right)z$$

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

$$\frac{11}{6}-\frac{1}{3}z=\frac{3}{4}-\frac{1}{4}z$$

Me tāpiri te \frac{1}{4}z ki ngā taha e rua.

$$\frac{11}{6}-\frac{1}{3}z+\frac{1}{4}z=\frac{3}{4}$$

Pahekotia te -\frac{1}{3}z me \frac{1}{4}z, ka -\frac{1}{12}z.

$$\frac{11}{6}-\frac{1}{12}z=\frac{3}{4}$$

Tangohia te \frac{11}{6} mai i ngā taha e rua.

$$-\frac{1}{12}z=\frac{3}{4}-\frac{11}{6}$$

Ko te maha noa iti rawa atu o 4 me 6 ko 12. Me tahuri \frac{3}{4} me \frac{11}{6} ki te hautau me te tautūnga 12.

$$-\frac{1}{12}z=\frac{9}{12}-\frac{22}{12}$$

Tā te mea he rite te tauraro o \frac{9}{12} me \frac{22}{12}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{1}{12}z=\frac{9-22}{12}$$

Tangohia te 22 i te 9, ka -13.

$$-\frac{1}{12}z=-\frac{13}{12}$$

Me whakarea ngā taha e rua ki te -12, te tau utu o -\frac{1}{12}.

$$z=-\frac{13}{12}\left(-12\right)$$

Tuhia te -\frac{13}{12}\left(-12\right) hei hautanga kotahi.

$$z=\frac{-13\left(-12\right)}{12}$$

Whakareatia te -13 ki te -12, ka 156.

$$z=\frac{156}{12}$$

Whakawehea te 156 ki te 12, kia riro ko 13.

$$z=13$$