Whakaoti i te 7(17/3-43):x=(5/4*8/10-4/9:2):(frac{5}{4}+frac{2}{5}-frac{1}{4})

$$7 ( \frac { 17 } { 3 } - 43 ) : x = ( \frac { 5 } { 4 } \cdot \frac { 8 } { 10 } - \frac { 4 } { 9 } : 2 ) : ( \frac { 5 } { 4 } + \frac { 2 } { 5 } - \frac { 1 } { 4 } )$$

Whakaoti mō x

$$x = -\frac{2352}{5} = -470\frac{2}{5} = -470.4$$

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.

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

Me tahuri te 43 ki te hautau \frac{129}{3}.

$$7\left(\frac{17}{3}-\frac{129}{3}\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Tā te mea he rite te tauraro o \frac{17}{3} me \frac{129}{3}, me tango rāua mā te tango i ō raua taurunga.

$$7\times \frac{17-129}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Tangohia te 129 i te 17, ka -112.

$$7\left(-\frac{112}{3}\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Tuhia te 7\left(-\frac{112}{3}\right) hei hautanga kotahi.

$$\frac{7\left(-112\right)}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Whakareatia te 7 ki te -112, ka -784.

$$\frac{-784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Ka taea te hautanga \frac{-784}{3} te tuhi anō ko -\frac{784}{3} mā te tango i te tohu tōraro.

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{4}{5}-\frac{\frac{4}{9}}{2}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{\frac{4}{9}}{2}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{4}{9\times 2}\right)$$

Whakareatia te 9 ki te 2, ka 18.

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{4}{18}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{2}{9}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{9}{9}-\frac{2}{9}\right)$$

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.

$$-\frac{784}{3}=\frac{5}{7}x\times \frac{9-2}{9}$$

Tangohia te 2 i te 9, ka 7.

$$-\frac{784}{3}=\frac{5}{7}x\times \frac{7}{9}$$

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

$$-\frac{784}{3}=\frac{5\times 7}{7\times 9}x$$

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

$$-\frac{784}{3}=\frac{5}{9}x$$

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

$$\frac{5}{9}x=-\frac{784}{3}$$

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

$$x=-\frac{784}{3}\times \frac{9}{5}$$

Me whakarea te -\frac{784}{3} ki te \frac{9}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-784\times 9}{3\times 5}$$

Mahia ngā whakarea i roto i te hautanga \frac{-784\times 9}{3\times 5}.

$$x=\frac{-7056}{15}$$

Whakahekea te hautanga \frac{-7056}{15} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=-\frac{2352}{5}$$