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

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

Whakaoti mō x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 4,3,2.

$$3x-12\left(\frac{2}{3}x-\left(\frac{1-x}{2}+1\right)\right)=9\left(1-x\right)$$

Hei kimi i te tauaro o \frac{1-x}{2}+1, kimihia te tauaro o ia taurangi.

$$3x-12\left(\frac{2}{3}x-\frac{1-x}{2}-1\right)=9\left(1-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te 1-x.

$$3x-12\left(\frac{2}{3}x-\frac{1-x}{2}-1\right)=9-9x$$

Whakawehea ia wā o 1-x ki te 2, kia riro ko \frac{1}{2}-\frac{1}{2}x.

$$3x-12\left(\frac{2}{3}x-\left(\frac{1}{2}-\frac{1}{2}x\right)-1\right)=9-9x$$

Hei kimi i te tauaro o \frac{1}{2}-\frac{1}{2}x, kimihia te tauaro o ia taurangi.

$$3x-12\left(\frac{2}{3}x-\frac{1}{2}-\left(-\frac{1}{2}x\right)-1\right)=9-9x$$

Ko te tauaro o -\frac{1}{2}x ko \frac{1}{2}x.

$$3x-12\left(\frac{2}{3}x-\frac{1}{2}+\frac{1}{2}x-1\right)=9-9x$$

Pahekotia te \frac{2}{3}x me \frac{1}{2}x, ka \frac{7}{6}x.

$$3x-12\left(\frac{7}{6}x-\frac{1}{2}-1\right)=9-9x$$

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

$$3x-12\left(\frac{7}{6}x-\frac{1}{2}-\frac{2}{2}\right)=9-9x$$

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.

$$3x-12\left(\frac{7}{6}x+\frac{-1-2}{2}\right)=9-9x$$

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

$$3x-12\left(\frac{7}{6}x-\frac{3}{2}\right)=9-9x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -12 ki te \frac{7}{6}x-\frac{3}{2}.

$$3x-12\times \frac{7}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

Tuhia te -12\times \frac{7}{6} hei hautanga kotahi.

$$3x+\frac{-12\times 7}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

Whakareatia te -12 ki te 7, ka -84.

$$3x+\frac{-84}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

Whakawehea te -84 ki te 6, kia riro ko -14.

$$3x-14x-12\left(-\frac{3}{2}\right)=9-9x$$

Tuhia te -12\left(-\frac{3}{2}\right) hei hautanga kotahi.

$$3x-14x+\frac{-12\left(-3\right)}{2}=9-9x$$

Whakareatia te -12 ki te -3, ka 36.

$$3x-14x+\frac{36}{2}=9-9x$$

Whakawehea te 36 ki te 2, kia riro ko 18.

$$3x-14x+18=9-9x$$

Pahekotia te 3x me -14x, ka -11x.

$$-11x+18=9-9x$$

Me tāpiri te 9x ki ngā taha e rua.

$$-11x+18+9x=9$$

Pahekotia te -11x me 9x, ka -2x.

$$-2x+18=9$$

Tangohia te 18 mai i ngā taha e rua.

$$-2x=9-18$$

Tangohia te 18 i te 9, ka -9.

$$-2x=-9$$

Whakawehea ngā taha e rua ki te -2.

$$x=\frac{-9}{-2}$$

Ka taea te hautanga \frac{-9}{-2} te whakamāmā ki te \frac{9}{2} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{9}{2}$$