Whakaoti i te {2/7x+9/2-[(4-5x/7-3x+4/2)-frac{9}{14}x]}-1=frac{3}{2}x

$$\{ \frac { 2 } { 7 } x + \frac { 9 } { 2 } - [ ( \frac { 4 - 5 x } { 7 } - \frac { 3 x + 4 } { 2 } ) - \frac { 9 } { 14 } x ] \} - 1 = \frac { 3 } { 2 } x$$

Whakaoti mō x

$$x=-3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 14, arā, te tauraro pātahi he tino iti rawa te kitea o 7,2,14.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{4-5x}{7}-\frac{3x+4}{2}-\frac{9}{14}x\right)\right)-14=21x$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 7 me 2 ko 14. Whakareatia \frac{4-5x}{7} ki te \frac{2}{2}. Whakareatia \frac{3x+4}{2} ki te \frac{7}{7}.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{2\left(4-5x\right)}{14}-\frac{7\left(3x+4\right)}{14}-\frac{9}{14}x\right)\right)-14=21x$$

Tā te mea he rite te tauraro o \frac{2\left(4-5x\right)}{14} me \frac{7\left(3x+4\right)}{14}, me tango rāua mā te tango i ō raua taurunga.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{2\left(4-5x\right)-7\left(3x+4\right)}{14}-\frac{9}{14}x\right)\right)-14=21x$$

Mahia ngā whakarea i roto o 2\left(4-5x\right)-7\left(3x+4\right).

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{8-10x-21x-28}{14}-\frac{9}{14}x\right)\right)-14=21x$$

Whakakotahitia ngā kupu rite i 8-10x-21x-28.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{-20-31x}{14}-\frac{9}{14}x\right)\right)-14=21x$$

Hei kimi i te tauaro o \frac{-20-31x}{14}-\frac{9}{14}x, kimihia te tauaro o ia taurangi.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\frac{-20-31x}{14}-\left(-\frac{9}{14}x\right)\right)-14=21x$$

Ko te tauaro o -\frac{9}{14}x ko \frac{9}{14}x.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\frac{-20-31x}{14}+\frac{9}{14}x\right)-14=21x$$

Pahekotia te \frac{2}{7}x me \frac{9}{14}x, ka \frac{13}{14}x.

$$14\left(\frac{13}{14}x+\frac{9}{2}-\frac{-20-31x}{14}\right)-14=21x$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me 14 ko 14. Whakareatia \frac{9}{2} ki te \frac{7}{7}.

$$14\left(\frac{13}{14}x+\frac{9\times 7}{14}-\frac{-20-31x}{14}\right)-14=21x$$

Tā te mea he rite te tauraro o \frac{9\times 7}{14} me \frac{-20-31x}{14}, me tango rāua mā te tango i ō raua taurunga.

$$14\left(\frac{13}{14}x+\frac{9\times 7-\left(-20-31x\right)}{14}\right)-14=21x$$

Mahia ngā whakarea i roto o 9\times 7-\left(-20-31x\right).

$$14\left(\frac{13}{14}x+\frac{63+20+31x}{14}\right)-14=21x$$

Whakakotahitia ngā kupu rite i 63+20+31x.

$$14\left(\frac{13}{14}x+\frac{83+31x}{14}\right)-14=21x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 14 ki te \frac{13}{14}x+\frac{83+31x}{14}.

$$14\times \frac{13}{14}x+14\times \frac{83+31x}{14}-14=21x$$

Me whakakore te 14 me te 14.

$$13x+14\times \frac{83+31x}{14}-14=21x$$

Tuhia te 14\times \frac{83+31x}{14} hei hautanga kotahi.

$$13x+\frac{14\left(83+31x\right)}{14}-14=21x$$

Me whakakore te 14 me te 14.

$$13x+83+31x-14=21x$$

Pahekotia te 13x me 31x, ka 44x.

$$44x+83-14=21x$$

Tangohia te 14 i te 83, ka 69.

$$44x+69=21x$$

Tangohia te 21x mai i ngā taha e rua.

$$44x+69-21x=0$$

Pahekotia te 44x me -21x, ka 23x.

$$23x+69=0$$

Tangohia te 69 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$23x=-69$$

Whakawehea ngā taha e rua ki te 23.

$$x=\frac{-69}{23}$$

Whakawehea te -69 ki te 23, kia riro ko -3.

$$x=-3$$