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

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

Whakaoti mō x

$$x=\frac{1}{4}=0.25$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Tuhia te \frac{2}{3}\times 6 hei hautanga kotahi.

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

Whakareatia te 2 ki te 6, ka 12.

$$\frac{12}{3}+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

Whakawehea te 12 ki te 3, kia riro ko 4.

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{3}{4} ki te 5-2x.

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

Tuhia te -\frac{3}{4}\times 5 hei hautanga kotahi.

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

Whakareatia te -3 ki te 5, ka -15.

$$4-\frac{2}{3}x+\frac{-15}{4}-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

Ka taea te hautanga \frac{-15}{4} te tuhi anō ko -\frac{15}{4} mā te tango i te tohu tōraro.

$$4-\frac{2}{3}x-\frac{15}{4}-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

Tuhia te -\frac{3}{4}\left(-2\right) hei hautanga kotahi.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{-3\left(-2\right)}{4}x=\frac{1}{6}\left(3-x\right)$$

Whakareatia te -3 ki te -2, ka 6.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{6}{4}x=\frac{1}{6}\left(3-x\right)$$

Whakahekea te hautanga \frac{6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

Me tahuri te 4 ki te hautau \frac{16}{4}.

$$\frac{16}{4}-\frac{2}{3}x-\frac{15}{4}+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

Tā te mea he rite te tauraro o \frac{16}{4} me \frac{15}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{16-15}{4}-\frac{2}{3}x+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

Tangohia te 15 i te 16, ka 1.

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

Pahekotia te -\frac{2}{3}x me \frac{3}{2}x, ka \frac{5}{6}x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{6} ki te 3-x.

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

Whakareatia te \frac{1}{6} ki te 3, ka \frac{3}{6}.

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

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

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

Whakareatia te \frac{1}{6} ki te -1, ka -\frac{1}{6}.

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{2}-\frac{1}{6}x$$

Me tāpiri te \frac{1}{6}x ki ngā taha e rua.

$$\frac{1}{4}+\frac{5}{6}x+\frac{1}{6}x=\frac{1}{2}$$

Pahekotia te \frac{5}{6}x me \frac{1}{6}x, ka x.

$$\frac{1}{4}+x=\frac{1}{2}$$

Tangohia te \frac{1}{4} mai i ngā taha e rua.

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

Ko te maha noa iti rawa atu o 2 me 4 ko 4. Me tahuri \frac{1}{2} me \frac{1}{4} ki te hautau me te tautūnga 4.

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

Tā te mea he rite te tauraro o \frac{2}{4} me \frac{1}{4}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 2, ka 1.

$$x=\frac{1}{4}$$