Whakaoti i te (8224-x)*(1+56%)=x

$$(8224-x) \times (1+56 \% )=x$$

Whakaoti mō x

$$x = \frac{10023}{2} = 5011\frac{1}{2} = 5011.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{56}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\left(8224-x\right)\left(1+\frac{14}{25}\right)=x$$

Me tahuri te 1 ki te hautau \frac{25}{25}.

$$\left(8224-x\right)\left(\frac{25}{25}+\frac{14}{25}\right)=x$$

Tā te mea he rite te tauraro o \frac{25}{25} me \frac{14}{25}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\left(8224-x\right)\times \frac{25+14}{25}=x$$

Tāpirihia te 25 ki te 14, ka 39.

$$\left(8224-x\right)\times \frac{39}{25}=x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8224-x ki te \frac{39}{25}.

$$8224\times \frac{39}{25}-x\times \frac{39}{25}=x$$

Tuhia te 8224\times \frac{39}{25} hei hautanga kotahi.

$$\frac{8224\times 39}{25}-x\times \frac{39}{25}=x$$

Whakareatia te 8224 ki te 39, ka 320736.

$$\frac{320736}{25}-x\times \frac{39}{25}=x$$

Whakareatia te -1 ki te \frac{39}{25}, ka -\frac{39}{25}.

$$\frac{320736}{25}-\frac{39}{25}x=x$$

Tangohia te x mai i ngā taha e rua.

$$\frac{320736}{25}-\frac{39}{25}x-x=0$$

Pahekotia te -\frac{39}{25}x me -x, ka -\frac{64}{25}x.

$$\frac{320736}{25}-\frac{64}{25}x=0$$

Tangohia te \frac{320736}{25} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-\frac{64}{25}x=-\frac{320736}{25}$$

Me whakarea ngā taha e rua ki te -\frac{25}{64}, te tau utu o -\frac{64}{25}.

$$x=-\frac{320736}{25}\left(-\frac{25}{64}\right)$$

Me whakarea te -\frac{320736}{25} ki te -\frac{25}{64} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-320736\left(-25\right)}{25\times 64}$$

Mahia ngā whakarea i roto i te hautanga \frac{-320736\left(-25\right)}{25\times 64}.

$$x=\frac{8018400}{1600}$$

Whakahekea te hautanga \frac{8018400}{1600} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 800.

$$x=\frac{10023}{2}$$