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

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

Whakaoti mō x

$$x=-\frac{5}{13}\approx -0.384615385$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

Pahekotia te x me -\frac{1}{2}x, ka \frac{1}{2}x.

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

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

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

Me whakarea te -\frac{1}{2} ki te \frac{1}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{-1}{2\times 2}.

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

Ka taea te hautanga \frac{-1}{4} te tuhi anō ko -\frac{1}{4} mā te tango i te tohu tōraro.

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

Me whakarea te -\frac{1}{2} ki te \frac{1}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{-1}{2\times 2}.

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

Ka taea te hautanga \frac{-1}{4} te tuhi anō ko -\frac{1}{4} mā te tango i te tohu tōraro.

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

Pahekotia te 2x me -\frac{1}{4}x, ka \frac{7}{4}x.

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}\left(x-1\right)$$

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

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}x+\frac{2}{3}\left(-1\right)$$

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

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}x-\frac{2}{3}$$

Tangohia te \frac{2}{3}x mai i ngā taha e rua.

$$\frac{7}{4}x-\frac{1}{4}-\frac{2}{3}x=-\frac{2}{3}$$

Pahekotia te \frac{7}{4}x me -\frac{2}{3}x, ka \frac{13}{12}x.

$$\frac{13}{12}x-\frac{1}{4}=-\frac{2}{3}$$

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

$$\frac{13}{12}x=-\frac{2}{3}+\frac{1}{4}$$

Ko te maha noa iti rawa atu o 3 me 4 ko 12. Me tahuri -\frac{2}{3} me \frac{1}{4} ki te hautau me te tautūnga 12.

$$\frac{13}{12}x=-\frac{8}{12}+\frac{3}{12}$$

Tā te mea he rite te tauraro o -\frac{8}{12} me \frac{3}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{13}{12}x=\frac{-8+3}{12}$$

Tāpirihia te -8 ki te 3, ka -5.

$$\frac{13}{12}x=-\frac{5}{12}$$

Me whakarea ngā taha e rua ki te \frac{12}{13}, te tau utu o \frac{13}{12}.

$$x=-\frac{5}{12}\times \frac{12}{13}$$

Me whakarea te -\frac{5}{12} ki te \frac{12}{13} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-5\times 12}{12\times 13}$$

Me whakakore tahi te 12 i te taurunga me te tauraro.

$$x=\frac{-5}{13}$$

Ka taea te hautanga \frac{-5}{13} te tuhi anō ko -\frac{5}{13} mā te tango i te tohu tōraro.

$$x=-\frac{5}{13}$$