Whakaoti i te 7(17/3-4.3):x=(5/4*8/10-4/9:2):(frac{5}{4}+frac{2}{5}-frac{1}{4})

$$7 ( \frac { 17 } { 3 } - 4.3 ) : x = ( \frac { 5 } { 4 } \cdot \frac { 8 } { 10 } - \frac { 4 } { 9 } : 2 ) : ( \frac { 5 } { 4 } + \frac { 2 } { 5 } - \frac { 1 } { 4 } )$$

Whakaoti mō x

$$x=17.22$$

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. Whakareatia ngā taha e rua o te whārite ki te x.

$$7\left(\frac{17}{3}-4.3\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Me tahuri ki tau ā-ira 4.3 ki te hautau \frac{43}{10}.

$$7\left(\frac{17}{3}-\frac{43}{10}\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Ko te maha noa iti rawa atu o 3 me 10 ko 30. Me tahuri \frac{17}{3} me \frac{43}{10} ki te hautau me te tautūnga 30.

$$7\left(\frac{170}{30}-\frac{129}{30}\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Tā te mea he rite te tauraro o \frac{170}{30} me \frac{129}{30}, me tango rāua mā te tango i ō raua taurunga.

$$7\times \frac{170-129}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Tangohia te 129 i te 170, ka 41.

$$7\times \frac{41}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Tuhia te 7\times \frac{41}{30} hei hautanga kotahi.

$$\frac{7\times 41}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Whakareatia te 7 ki te 41, ka 287.

$$\frac{287}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Whakahekea te hautanga \frac{8}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{287}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{4}{5}-\frac{\frac{4}{9}}{2}\right)$$

Me whakakore atu te \frac{5}{4} me tōna tau utu \frac{4}{5}.

$$\frac{287}{30}=\frac{5}{7}x\left(1-\frac{\frac{4}{9}}{2}\right)$$

Tuhia te \frac{\frac{4}{9}}{2} hei hautanga kotahi.

$$\frac{287}{30}=\frac{5}{7}x\left(1-\frac{4}{9\times 2}\right)$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{287}{30}=\frac{5}{7}x\left(1-\frac{4}{18}\right)$$

Whakahekea te hautanga \frac{4}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{287}{30}=\frac{5}{7}x\left(1-\frac{2}{9}\right)$$

Me tahuri te 1 ki te hautau \frac{9}{9}.

$$\frac{287}{30}=\frac{5}{7}x\left(\frac{9}{9}-\frac{2}{9}\right)$$

Tā te mea he rite te tauraro o \frac{9}{9} me \frac{2}{9}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{287}{30}=\frac{5}{7}x\times \frac{9-2}{9}$$

Tangohia te 2 i te 9, ka 7.

$$\frac{287}{30}=\frac{5}{7}x\times \frac{7}{9}$$

Me whakarea te \frac{5}{7} ki te \frac{7}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{287}{30}=\frac{5\times 7}{7\times 9}x$$

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

$$\frac{287}{30}=\frac{5}{9}x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{5}{9}x=\frac{287}{30}$$

Me whakarea ngā taha e rua ki te \frac{9}{5}, te tau utu o \frac{5}{9}.

$$x=\frac{287}{30}\times \frac{9}{5}$$

Me whakarea te \frac{287}{30} ki te \frac{9}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{287\times 9}{30\times 5}$$

Mahia ngā whakarea i roto i te hautanga \frac{287\times 9}{30\times 5}.

$$x=\frac{2583}{150}$$

Whakahekea te hautanga \frac{2583}{150} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=\frac{861}{50}$$