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

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

Whakaoti mō x

$$x = -\frac{13}{5} = -2\frac{3}{5} = -2.6$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

Ka taea te hautanga \frac{-3}{2} te tuhi anō ko -\frac{3}{2} mā te tango i te tohu tōraro.

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

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

$$\frac{1}{2}x-\frac{3}{2}-\frac{1}{3}x-\frac{1}{3}\times 2=x$$

Tuhia te -\frac{1}{3}\times 2 hei hautanga kotahi.

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

Ka taea te hautanga \frac{-2}{3} te tuhi anō ko -\frac{2}{3} mā te tango i te tohu tōraro.

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

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

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

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri -\frac{3}{2} me \frac{2}{3} ki te hautau me te tautūnga 6.

$$\frac{1}{6}x-\frac{9}{6}-\frac{4}{6}=x$$

Tā te mea he rite te tauraro o -\frac{9}{6} me \frac{4}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{6}x+\frac{-9-4}{6}=x$$

Tangohia te 4 i te -9, ka -13.

$$\frac{1}{6}x-\frac{13}{6}=x$$

Tangohia te x mai i ngā taha e rua.

$$\frac{1}{6}x-\frac{13}{6}-x=0$$

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

$$-\frac{5}{6}x-\frac{13}{6}=0$$

Me tāpiri te \frac{13}{6} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-\frac{5}{6}x=\frac{13}{6}$$

Me whakarea ngā taha e rua ki te -\frac{6}{5}, te tau utu o -\frac{5}{6}.

$$x=\frac{13}{6}\left(-\frac{6}{5}\right)$$

Me whakarea te \frac{13}{6} ki te -\frac{6}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{13\left(-6\right)}{6\times 5}$$

Mahia ngā whakarea i roto i te hautanga \frac{13\left(-6\right)}{6\times 5}.

$$x=\frac{-78}{30}$$

Whakahekea te hautanga \frac{-78}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

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