Whakaoti i te 1/8+1/x=1/4.5

$$\frac { 1 } { 8 } + \frac { 1 } { x } = \frac { 1 } { 4.5 }$$

Whakaoti mō x

$$x = \frac{72}{7} = 10\frac{2}{7} \approx 10.285714286$$

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 8x, arā, te tauraro pātahi he tino iti rawa te kitea o 8,x.

$$8x\times \frac{1}{8}+8=8x\times \frac{1}{4.5}$$

Me whakakore te 8 me te 8.

$$x+8=8x\times \frac{1}{4.5}$$

Whakarohaina te \frac{1}{4.5} mā te whakarea i te taurunga me te tauraro ki te 10.

$$x+8=8x\times \frac{10}{45}$$

Whakahekea te hautanga \frac{10}{45} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x+8=8x\times \frac{2}{9}$$

Tuhia te 8\times \frac{2}{9} hei hautanga kotahi.

$$x+8=\frac{8\times 2}{9}x$$

Whakareatia te 8 ki te 2, ka 16.

$$x+8=\frac{16}{9}x$$

Tangohia te \frac{16}{9}x mai i ngā taha e rua.

$$x+8-\frac{16}{9}x=0$$

Pahekotia te x me -\frac{16}{9}x, ka -\frac{7}{9}x.

$$-\frac{7}{9}x+8=0$$

Tangohia te 8 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-\frac{7}{9}x=-8$$

Me whakarea ngā taha e rua ki te -\frac{9}{7}, te tau utu o -\frac{7}{9}.

$$x=-8\left(-\frac{9}{7}\right)$$

Tuhia te -8\left(-\frac{9}{7}\right) hei hautanga kotahi.

$$x=\frac{-8\left(-9\right)}{7}$$

Whakareatia te -8 ki te -9, ka 72.

$$x=\frac{72}{7}$$