Whakaoti i te 3+2x/5-(2-3-x/3)=x

$$\frac { 3 + 2 x } { 5 } - ( 2 - \frac { 3 - x } { 3 } ) = x$$

Whakaoti mō x

$$x=-\frac{3}{7}\approx -0.428571429$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Hei kimi i te tauaro o 2-\frac{3-x}{3}, kimihia te tauaro o ia taurangi.

$$\frac{3+2x}{5}-2-\left(-\frac{3-x}{3}\right)=x$$

Whakawehea ia wā o 3+2x ki te 5, kia riro ko \frac{3}{5}+\frac{2}{5}x.

$$\frac{3}{5}+\frac{2}{5}x-2-\left(-\frac{3-x}{3}\right)=x$$

Me tahuri te 2 ki te hautau \frac{10}{5}.

$$\frac{3}{5}+\frac{2}{5}x-\frac{10}{5}-\left(-\frac{3-x}{3}\right)=x$$

Tā te mea he rite te tauraro o \frac{3}{5} me \frac{10}{5}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3-10}{5}+\frac{2}{5}x-\left(-\frac{3-x}{3}\right)=x$$

Tangohia te 10 i te 3, ka -7.

$$-\frac{7}{5}+\frac{2}{5}x-\left(-\frac{3-x}{3}\right)=x$$

Whakawehea ia wā o 3-x ki te 3, kia riro ko 1-\frac{1}{3}x.

$$-\frac{7}{5}+\frac{2}{5}x-\left(-\left(1-\frac{1}{3}x\right)\right)=x$$

Hei kimi i te tauaro o 1-\frac{1}{3}x, kimihia te tauaro o ia taurangi.

$$-\frac{7}{5}+\frac{2}{5}x-\left(-1-\left(-\frac{1}{3}x\right)\right)=x$$

Ko te tauaro o -\frac{1}{3}x ko \frac{1}{3}x.

$$-\frac{7}{5}+\frac{2}{5}x-\left(-1+\frac{1}{3}x\right)=x$$

Hei kimi i te tauaro o -1+\frac{1}{3}x, kimihia te tauaro o ia taurangi.

$$-\frac{7}{5}+\frac{2}{5}x-\left(-1\right)-\frac{1}{3}x=x$$

Ko te tauaro o -1 ko 1.

$$-\frac{7}{5}+\frac{2}{5}x+1-\frac{1}{3}x=x$$

Me tahuri te 1 ki te hautau \frac{5}{5}.

$$-\frac{7}{5}+\frac{2}{5}x+\frac{5}{5}-\frac{1}{3}x=x$$

Tā te mea he rite te tauraro o -\frac{7}{5} me \frac{5}{5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-7+5}{5}+\frac{2}{5}x-\frac{1}{3}x=x$$

Tāpirihia te -7 ki te 5, ka -2.

$$-\frac{2}{5}+\frac{2}{5}x-\frac{1}{3}x=x$$

Pahekotia te \frac{2}{5}x me -\frac{1}{3}x, ka \frac{1}{15}x.

$$-\frac{2}{5}+\frac{1}{15}x=x$$

Tangohia te x mai i ngā taha e rua.

$$-\frac{2}{5}+\frac{1}{15}x-x=0$$

Pahekotia te \frac{1}{15}x me -x, ka -\frac{14}{15}x.

$$-\frac{2}{5}-\frac{14}{15}x=0$$

Me tāpiri te \frac{2}{5} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-\frac{14}{15}x=\frac{2}{5}$$

Me whakarea ngā taha e rua ki te -\frac{15}{14}, te tau utu o -\frac{14}{15}.

$$x=\frac{2}{5}\left(-\frac{15}{14}\right)$$

Me whakarea te \frac{2}{5} ki te -\frac{15}{14} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{2\left(-15\right)}{5\times 14}$$

Mahia ngā whakarea i roto i te hautanga \frac{2\left(-15\right)}{5\times 14}.

$$x=\frac{-30}{70}$$

Whakahekea te hautanga \frac{-30}{70} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$x=-\frac{3}{7}$$