Whakaoti i te 5-2/5(x+24)=-3/4(15+x)

$$5- \frac{ 2 }{ 5 } (x+24)=- \frac{ 3 }{ 4 } (15+x)$$

Whakaoti mō x

$$x=-19$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{2}{5} ki te x+24.

$$5-\frac{2}{5}x-\frac{2}{5}\times 24=-\frac{3}{4}\left(15+x\right)$$

Tuhia te -\frac{2}{5}\times 24 hei hautanga kotahi.

$$5-\frac{2}{5}x+\frac{-2\times 24}{5}=-\frac{3}{4}\left(15+x\right)$$

Whakareatia te -2 ki te 24, ka -48.

$$5-\frac{2}{5}x+\frac{-48}{5}=-\frac{3}{4}\left(15+x\right)$$

Ka taea te hautanga \frac{-48}{5} te tuhi anō ko -\frac{48}{5} mā te tango i te tohu tōraro.

$$5-\frac{2}{5}x-\frac{48}{5}=-\frac{3}{4}\left(15+x\right)$$

Me tahuri te 5 ki te hautau \frac{25}{5}.

$$\frac{25}{5}-\frac{2}{5}x-\frac{48}{5}=-\frac{3}{4}\left(15+x\right)$$

Tā te mea he rite te tauraro o \frac{25}{5} me \frac{48}{5}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{25-48}{5}-\frac{2}{5}x=-\frac{3}{4}\left(15+x\right)$$

Tangohia te 48 i te 25, ka -23.

$$-\frac{23}{5}-\frac{2}{5}x=-\frac{3}{4}\left(15+x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{3}{4} ki te 15+x.

$$-\frac{23}{5}-\frac{2}{5}x=-\frac{3}{4}\times 15-\frac{3}{4}x$$

Tuhia te -\frac{3}{4}\times 15 hei hautanga kotahi.

$$-\frac{23}{5}-\frac{2}{5}x=\frac{-3\times 15}{4}-\frac{3}{4}x$$

Whakareatia te -3 ki te 15, ka -45.

$$-\frac{23}{5}-\frac{2}{5}x=\frac{-45}{4}-\frac{3}{4}x$$

Ka taea te hautanga \frac{-45}{4} te tuhi anō ko -\frac{45}{4} mā te tango i te tohu tōraro.

$$-\frac{23}{5}-\frac{2}{5}x=-\frac{45}{4}-\frac{3}{4}x$$

Me tāpiri te \frac{3}{4}x ki ngā taha e rua.

$$-\frac{23}{5}-\frac{2}{5}x+\frac{3}{4}x=-\frac{45}{4}$$

Pahekotia te -\frac{2}{5}x me \frac{3}{4}x, ka \frac{7}{20}x.

$$-\frac{23}{5}+\frac{7}{20}x=-\frac{45}{4}$$

Me tāpiri te \frac{23}{5} ki ngā taha e rua.

$$\frac{7}{20}x=-\frac{45}{4}+\frac{23}{5}$$

Ko te maha noa iti rawa atu o 4 me 5 ko 20. Me tahuri -\frac{45}{4} me \frac{23}{5} ki te hautau me te tautūnga 20.

$$\frac{7}{20}x=-\frac{225}{20}+\frac{92}{20}$$

Tā te mea he rite te tauraro o -\frac{225}{20} me \frac{92}{20}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7}{20}x=\frac{-225+92}{20}$$

Tāpirihia te -225 ki te 92, ka -133.

$$\frac{7}{20}x=-\frac{133}{20}$$

Me whakarea ngā taha e rua ki te \frac{20}{7}, te tau utu o \frac{7}{20}.

$$x=-\frac{133}{20}\times \frac{20}{7}$$

Me whakarea te -\frac{133}{20} ki te \frac{20}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-133\times 20}{20\times 7}$$

Me whakakore tahi te 20 i te taurunga me te tauraro.

$$x=\frac{-133}{7}$$

Whakawehea te -133 ki te 7, kia riro ko -19.

$$x=-19$$