Whakaoti i te (x-21/3*(-31/7)*(-22/11)/1frac{1{9}*(-1frac{1}{8})*16}):(-frac{1}{3})=6

$$( x - \frac { 2 \frac { 1 } { 3 } \cdot ( - 3 \frac { 1 } { 7 } ) \cdot ( - 2 \frac { 2 } { 11 } ) } { 1 \frac { 1 } { 9 } \cdot ( - 1 \frac { 1 } { 8 } ) \cdot 16 } ) : ( - \frac { 1 } { 3 } ) = 6$$

Whakaoti mō x

$$x = -\frac{14}{5} = -2\frac{4}{5} = -2.8$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua ki te -\frac{1}{3}.

$$x-\frac{\frac{2\times 3+1}{3}\left(-\frac{3\times 7+1}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Whakareatia te 2 ki te 3, ka 6.

$$x-\frac{\frac{6+1}{3}\left(-\frac{3\times 7+1}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Tāpirihia te 6 ki te 1, ka 7.

$$x-\frac{\frac{7}{3}\left(-\frac{3\times 7+1}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Whakareatia te 3 ki te 7, ka 21.

$$x-\frac{\frac{7}{3}\left(-\frac{21+1}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Tāpirihia te 21 ki te 1, ka 22.

$$x-\frac{\frac{7}{3}\left(-\frac{22}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Me whakarea te \frac{7}{3} ki te -\frac{22}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x-\frac{\frac{7\left(-22\right)}{3\times 7}\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Me whakakore tahi te 7 i te taurunga me te tauraro.

$$x-\frac{\frac{-22}{3}\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Ka taea te hautanga \frac{-22}{3} te tuhi anō ko -\frac{22}{3} mā te tango i te tohu tōraro.

$$x-\frac{-\frac{22}{3}\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Whakareatia te 2 ki te 11, ka 22.

$$x-\frac{-\frac{22}{3}\left(-\frac{22+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Tāpirihia te 22 ki te 2, ka 24.

$$x-\frac{-\frac{22}{3}\left(-\frac{24}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Me whakarea te -\frac{22}{3} ki te -\frac{24}{11} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x-\frac{\frac{-22\left(-24\right)}{3\times 11}}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{-22\left(-24\right)}{3\times 11}.

$$x-\frac{\frac{528}{33}}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Whakawehea te 528 ki te 33, kia riro ko 16.

$$x-\frac{16}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Whakareatia te 1 ki te 9, ka 9.

$$x-\frac{16}{\frac{9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Tāpirihia te 9 ki te 1, ka 10.

$$x-\frac{16}{\frac{10}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Whakareatia te 1 ki te 8, ka 8.

$$x-\frac{16}{\frac{10}{9}\left(-\frac{8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Tāpirihia te 8 ki te 1, ka 9.

$$x-\frac{16}{\frac{10}{9}\left(-\frac{9}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Me whakarea te \frac{10}{9} ki te -\frac{9}{8} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x-\frac{16}{\frac{10\left(-9\right)}{9\times 8}\times 16}=6\left(-\frac{1}{3}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{10\left(-9\right)}{9\times 8}.

$$x-\frac{16}{\frac{-90}{72}\times 16}=6\left(-\frac{1}{3}\right)$$

Whakahekea te hautanga \frac{-90}{72} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 18.

$$x-\frac{16}{-\frac{5}{4}\times 16}=6\left(-\frac{1}{3}\right)$$

Tuhia te -\frac{5}{4}\times 16 hei hautanga kotahi.

$$x-\frac{16}{\frac{-5\times 16}{4}}=6\left(-\frac{1}{3}\right)$$

Whakareatia te -5 ki te 16, ka -80.

$$x-\frac{16}{\frac{-80}{4}}=6\left(-\frac{1}{3}\right)$$

Whakawehea te -80 ki te 4, kia riro ko -20.

$$x-\frac{16}{-20}=6\left(-\frac{1}{3}\right)$$

Whakahekea te hautanga \frac{16}{-20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x-\left(-\frac{4}{5}\right)=6\left(-\frac{1}{3}\right)$$

Ko te tauaro o -\frac{4}{5} ko \frac{4}{5}.

$$x+\frac{4}{5}=6\left(-\frac{1}{3}\right)$$

Tuhia te 6\left(-\frac{1}{3}\right) hei hautanga kotahi.

$$x+\frac{4}{5}=\frac{6\left(-1\right)}{3}$$

Whakareatia te 6 ki te -1, ka -6.

$$x+\frac{4}{5}=\frac{-6}{3}$$

Whakawehea te -6 ki te 3, kia riro ko -2.

$$x+\frac{4}{5}=-2$$

Tangohia te \frac{4}{5} mai i ngā taha e rua.

$$x=-2-\frac{4}{5}$$

Me tahuri te -2 ki te hautau -\frac{10}{5}.

$$x=-\frac{10}{5}-\frac{4}{5}$$

Tā te mea he rite te tauraro o -\frac{10}{5} me \frac{4}{5}, me tango rāua mā te tango i ō raua taurunga.

$$x=\frac{-10-4}{5}$$

Tangohia te 4 i te -10, ka -14.

$$x=-\frac{14}{5}$$