Whakaoti i te 1/2(x+1/3)+1/4(2/3x-frac{1}{6})=x

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

Whakaoti mō x

$$x=\frac{3}{8}=0.375$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Me whakarea te \frac{1}{2} ki te \frac{1}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{1\times 1}{2\times 3}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te \frac{2}{3}x-\frac{1}{6}.

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

Me whakarea te \frac{1}{4} ki te \frac{2}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{1\times 2}{4\times 3}.

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

Whakahekea te hautanga \frac{2}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Me whakarea te \frac{1}{4} ki te -\frac{1}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{1\left(-1\right)}{4\times 6}.

$$\frac{1}{2}x+\frac{1}{6}+\frac{1}{6}x+\frac{-1}{24}=x$$

Ka taea te hautanga \frac{-1}{24} te tuhi anō ko -\frac{1}{24} mā te tango i te tohu tōraro.

$$\frac{1}{2}x+\frac{1}{6}+\frac{1}{6}x-\frac{1}{24}=x$$

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

$$\frac{2}{3}x+\frac{1}{6}-\frac{1}{24}=x$$

Ko te maha noa iti rawa atu o 6 me 24 ko 24. Me tahuri \frac{1}{6} me \frac{1}{24} ki te hautau me te tautūnga 24.

$$\frac{2}{3}x+\frac{4}{24}-\frac{1}{24}=x$$

Tā te mea he rite te tauraro o \frac{4}{24} me \frac{1}{24}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2}{3}x+\frac{4-1}{24}=x$$

Tangohia te 1 i te 4, ka 3.

$$\frac{2}{3}x+\frac{3}{24}=x$$

Whakahekea te hautanga \frac{3}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{2}{3}x+\frac{1}{8}=x$$

Tangohia te x mai i ngā taha e rua.

$$\frac{2}{3}x+\frac{1}{8}-x=0$$

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

$$-\frac{1}{3}x+\frac{1}{8}=0$$

Tangohia te \frac{1}{8} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-\frac{1}{3}x=-\frac{1}{8}$$

Me whakarea ngā taha e rua ki te -3, te tau utu o -\frac{1}{3}.

$$x=-\frac{1}{8}\left(-3\right)$$

Tuhia te -\frac{1}{8}\left(-3\right) hei hautanga kotahi.

$$x=\frac{-\left(-3\right)}{8}$$

Whakareatia te -1 ki te -3, ka 3.

$$x=\frac{3}{8}$$