Whakaoti i te 1/5x-[2/3x-(1-x/2+4)]=3/4(1-x)

$$\frac { 1 } { 5 } x - [ \frac { 2 } { 3 } x - ( \frac { 1 - x } { 2 } + 4 ) ] = \frac { 3 } { 4 } ( 1 - x )$$

Whakaoti mō x

$$x = \frac{225}{13} = 17\frac{4}{13} \approx 17.307692308$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 60, arā, te tauraro pātahi he tino iti rawa te kitea o 5,3,2,4.

$$12x-60\left(\frac{2}{3}x-\left(\frac{1-x}{2}+4\right)\right)=45\left(1-x\right)$$

Hei kimi i te tauaro o \frac{1-x}{2}+4, kimihia te tauaro o ia taurangi.

$$12x-60\left(\frac{2}{3}x-\frac{1-x}{2}-4\right)=45\left(1-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 45 ki te 1-x.

$$12x-60\left(\frac{2}{3}x-\frac{1-x}{2}-4\right)=45-45x$$

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

$$12x-60\left(\frac{2}{3}x-\left(\frac{1}{2}-\frac{1}{2}x\right)-4\right)=45-45x$$

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

$$12x-60\left(\frac{2}{3}x-\frac{1}{2}-\left(-\frac{1}{2}x\right)-4\right)=45-45x$$

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

$$12x-60\left(\frac{2}{3}x-\frac{1}{2}+\frac{1}{2}x-4\right)=45-45x$$

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

$$12x-60\left(\frac{7}{6}x-\frac{1}{2}-4\right)=45-45x$$

Me tahuri te 4 ki te hautau \frac{8}{2}.

$$12x-60\left(\frac{7}{6}x-\frac{1}{2}-\frac{8}{2}\right)=45-45x$$

Tā te mea he rite te tauraro o -\frac{1}{2} me \frac{8}{2}, me tango rāua mā te tango i ō raua taurunga.

$$12x-60\left(\frac{7}{6}x+\frac{-1-8}{2}\right)=45-45x$$

Tangohia te 8 i te -1, ka -9.

$$12x-60\left(\frac{7}{6}x-\frac{9}{2}\right)=45-45x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -60 ki te \frac{7}{6}x-\frac{9}{2}.

$$12x-60\times \frac{7}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

Tuhia te -60\times \frac{7}{6} hei hautanga kotahi.

$$12x+\frac{-60\times 7}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

Whakareatia te -60 ki te 7, ka -420.

$$12x+\frac{-420}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

Whakawehea te -420 ki te 6, kia riro ko -70.

$$12x-70x-60\left(-\frac{9}{2}\right)=45-45x$$

Tuhia te -60\left(-\frac{9}{2}\right) hei hautanga kotahi.

$$12x-70x+\frac{-60\left(-9\right)}{2}=45-45x$$

Whakareatia te -60 ki te -9, ka 540.

$$12x-70x+\frac{540}{2}=45-45x$$

Whakawehea te 540 ki te 2, kia riro ko 270.

$$12x-70x+270=45-45x$$

Pahekotia te 12x me -70x, ka -58x.

$$-58x+270=45-45x$$

Me tāpiri te 45x ki ngā taha e rua.

$$-58x+270+45x=45$$

Pahekotia te -58x me 45x, ka -13x.

$$-13x+270=45$$

Tangohia te 270 mai i ngā taha e rua.

$$-13x=45-270$$

Tangohia te 270 i te 45, ka -225.

$$-13x=-225$$

Whakawehea ngā taha e rua ki te -13.

$$x=\frac{-225}{-13}$$

Ka taea te hautanga \frac{-225}{-13} te whakamāmā ki te \frac{225}{13} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{225}{13}$$