Whakaoti i te 62/3/x-8=-4.2*5/7-3

$$\frac{ 6 \frac{ 2 }{ 3 } }{ x } -8 = -4.2 \times \frac{ 5 }{ 7 } -3$$

Whakaoti mō x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

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.

$$7\times \frac{6\times 3+2}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Whakareatia te 6 ki te 3, ka 18.

$$7\times \frac{18+2}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Tāpirihia te 18 ki te 2, ka 20.

$$7\times \frac{20}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

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

$$\frac{7\times 20}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Whakareatia te 7 ki te 20, ka 140.

$$\frac{140}{3}+7x\left(-8\right)=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

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

$$\frac{140}{3}-56x=-4.2\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Me tahuri ki tau ā-ira -4.2 ki te hautau -\frac{42}{10}. Whakahekea te hautanga -\frac{42}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{140}{3}-56x=-\frac{21}{5}\times \frac{5}{7}\times 7x+7x\left(-3\right)$$

Me whakarea te -\frac{21}{5} ki te \frac{5}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{140}{3}-56x=\frac{-21\times 5}{5\times 7}\times 7x+7x\left(-3\right)$$

Me whakakore tahi te 5 i te taurunga me te tauraro.

$$\frac{140}{3}-56x=\frac{-21}{7}\times 7x+7x\left(-3\right)$$

Whakawehea te -21 ki te 7, kia riro ko -3.

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

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

$$\frac{140}{3}-56x=-21x+7x\left(-3\right)$$

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

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

Pahekotia te -21x me -21x, ka -42x.

$$\frac{140}{3}-56x=-42x$$

Me tāpiri te 42x ki ngā taha e rua.

$$\frac{140}{3}-56x+42x=0$$

Pahekotia te -56x me 42x, ka -14x.

$$\frac{140}{3}-14x=0$$

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

$$-14x=-\frac{140}{3}$$

Whakawehea ngā taha e rua ki te -14.

$$x=\frac{-\frac{140}{3}}{-14}$$

Tuhia te \frac{-\frac{140}{3}}{-14} hei hautanga kotahi.

$$x=\frac{-140}{3\left(-14\right)}$$

Whakareatia te 3 ki te -14, ka -42.

$$x=\frac{-140}{-42}$$

Whakahekea te hautanga \frac{-140}{-42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -14.

$$x=\frac{10}{3}$$