Whakaoti i te 3/5x-1/4-3/2x=3/5-frac{9}{4x}

$$\frac { 3 } { 5 x } - \frac { 1 } { 4 } - \frac { 3 } { 2 x } = \frac { 3 } { 5 } - \frac { 9 } { 4 x }$$

Whakaoti mō x

$$x = \frac{27}{17} = 1\frac{10}{17} \approx 1.588235294$$

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 20x, arā, te tauraro pātahi he tino iti rawa te kitea o 5x,4,2x,5,4x.

$$4\times 3+20x\left(-\frac{1}{4}\right)-10\times 3=20x\times \frac{3}{5}-5\times 9$$

Mahia ngā whakarea.

$$12+20x\left(-\frac{1}{4}\right)-30=20x\times \frac{3}{5}-5\times 9$$

Whakareatia te 20 ki te -\frac{1}{4}, ka -5.

$$12-5x-30=20x\times \frac{3}{5}-5\times 9$$

Tangohia te 30 i te 12, ka -18.

$$-18-5x=20x\times \frac{3}{5}-5\times 9$$

Whakareatia te 20 ki te \frac{3}{5}, ka 12.

$$-18-5x=12x-5\times 9$$

Whakareatia te -5 ki te 9, ka -45.

$$-18-5x=12x-45$$

Tangohia te 12x mai i ngā taha e rua.

$$-18-5x-12x=-45$$

Pahekotia te -5x me -12x, ka -17x.

$$-18-17x=-45$$

Me tāpiri te 18 ki ngā taha e rua.

$$-17x=-45+18$$

Tāpirihia te -45 ki te 18, ka -27.

$$-17x=-27$$

Whakawehea ngā taha e rua ki te -17.

$$x=\frac{-27}{-17}$$

Ka taea te hautanga \frac{-27}{-17} te whakamāmā ki te \frac{27}{17} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{27}{17}$$