Whakaoti i te 3/2x-7/5=4/5x-5/2

$$\frac { 3 } { 2 x } - \frac { 7 } { 5 } = \frac { 4 } { 5 x } - \frac { 5 } { 2 }$$

Whakaoti mō x

$$x=-\frac{7}{11}\approx -0.636363636$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10x, arā, te tauraro pātahi he tino iti rawa te kitea o 2x,5,5x,2.

$$5\times 3+10x\left(-\frac{7}{5}\right)=2\times 4+10x\left(-\frac{5}{2}\right)$$

Whakareatia te 5 ki te 3, ka 15.

$$15+10x\left(-\frac{7}{5}\right)=2\times 4+10x\left(-\frac{5}{2}\right)$$

Whakareatia te 10 ki te -\frac{7}{5}, ka -14.

$$15-14x=2\times 4+10x\left(-\frac{5}{2}\right)$$

Whakareatia te 2 ki te 4, ka 8.

$$15-14x=8+10x\left(-\frac{5}{2}\right)$$

Whakareatia te 10 ki te -\frac{5}{2}, ka -25.

$$15-14x=8-25x$$

Me tāpiri te 25x ki ngā taha e rua.

$$15-14x+25x=8$$

Pahekotia te -14x me 25x, ka 11x.

$$15+11x=8$$

Tangohia te 15 mai i ngā taha e rua.

$$11x=8-15$$

Tangohia te 15 i te 8, ka -7.

$$11x=-7$$

Whakawehea ngā taha e rua ki te 11.

$$x=\frac{-7}{11}$$

Ka taea te hautanga \frac{-7}{11} te tuhi anō ko -\frac{7}{11} mā te tango i te tohu tōraro.

$$x=-\frac{7}{11}$$