Whakaoti i te 62/3/x-8=-42*5/7-3

$$\frac{ 6 \frac{ 2 }{ 3 } }{ x } -8 = -42 \times \frac{ 5 }{ 7 } -3$$

Whakaoti mō x

$$x=-\frac{4}{15}\approx -0.266666667$$

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 7x, arā, te tauraro pātahi he tino iti rawa te kitea o x,7.

$$7\times \frac{6\times 3+2}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Whakareatia te 6 ki te 3, ka 18.

$$7\times \frac{18+2}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Tāpirihia te 18 ki te 2, ka 20.

$$7\times \frac{20}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Tuhia te 7\times \frac{20}{3} hei hautanga kotahi.

$$\frac{7\times 20}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Whakareatia te 7 ki te 20, ka 140.

$$\frac{140}{3}+7x\left(-8\right)=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Whakareatia te 7 ki te -8, ka -56.

$$\frac{140}{3}-56x=-42\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Tuhia te -42\times \frac{5}{7} hei hautanga kotahi.

$$\frac{140}{3}-56x=\frac{-42\times 5}{7}\times 7x+7x\left(-3\right)$$

Whakareatia te -42 ki te 5, ka -210.

$$\frac{140}{3}-56x=\frac{-210}{7}\times 7x+7x\left(-3\right)$$

Whakawehea te -210 ki te 7, kia riro ko -30.

$$\frac{140}{3}-56x=-30\times 7x+7x\left(-3\right)$$

Whakareatia te -30 ki te 7, ka -210.

$$\frac{140}{3}-56x=-210x+7x\left(-3\right)$$

Whakareatia te 7 ki te -3, ka -21.

$$\frac{140}{3}-56x=-210x-21x$$

Pahekotia te -210x me -21x, ka -231x.

$$\frac{140}{3}-56x=-231x$$

Me tāpiri te 231x ki ngā taha e rua.

$$\frac{140}{3}-56x+231x=0$$

Pahekotia te -56x me 231x, ka 175x.

$$\frac{140}{3}+175x=0$$

Tangohia te \frac{140}{3} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$175x=-\frac{140}{3}$$

Whakawehea ngā taha e rua ki te 175.

$$x=\frac{-\frac{140}{3}}{175}$$

Tuhia te \frac{-\frac{140}{3}}{175} hei hautanga kotahi.

$$x=\frac{-140}{3\times 175}$$

Whakareatia te 3 ki te 175, ka 525.

$$x=\frac{-140}{525}$$

Whakahekea te hautanga \frac{-140}{525} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 35.

$$x=-\frac{4}{15}$$