Whakaoti i te 12/5(r-2)=2/3[3r-2(2r-1)]

$$\frac { 12 } { 5 } ( r - 2 ) = \frac { 2 } { 3 } [ 3 r - 2 ( 2 r - 1 ) ]$$

Whakaoti mō r

$$r=2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{12}{5} ki te r-2.

$$\frac{12}{5}r+\frac{12}{5}\left(-2\right)=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

Tuhia te \frac{12}{5}\left(-2\right) hei hautanga kotahi.

$$\frac{12}{5}r+\frac{12\left(-2\right)}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

Whakareatia te 12 ki te -2, ka -24.

$$\frac{12}{5}r+\frac{-24}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

Ka taea te hautanga \frac{-24}{5} te tuhi anō ko -\frac{24}{5} mā te tango i te tohu tōraro.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 2r-1.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(3r-4r+2\right)$$

Pahekotia te 3r me -4r, ka -r.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(-r+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{2}{3} ki te -r+2.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(-1\right)r+\frac{2}{3}\times 2$$

Whakareatia te \frac{2}{3} ki te -1, ka -\frac{2}{3}.

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{2}{3}\times 2$$

Tuhia te \frac{2}{3}\times 2 hei hautanga kotahi.

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{2\times 2}{3}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{4}{3}$$

Me tāpiri te \frac{2}{3}r ki ngā taha e rua.

$$\frac{12}{5}r-\frac{24}{5}+\frac{2}{3}r=\frac{4}{3}$$

Pahekotia te \frac{12}{5}r me \frac{2}{3}r, ka \frac{46}{15}r.

$$\frac{46}{15}r-\frac{24}{5}=\frac{4}{3}$$

Me tāpiri te \frac{24}{5} ki ngā taha e rua.

$$\frac{46}{15}r=\frac{4}{3}+\frac{24}{5}$$

Ko te maha noa iti rawa atu o 3 me 5 ko 15. Me tahuri \frac{4}{3} me \frac{24}{5} ki te hautau me te tautūnga 15.

$$\frac{46}{15}r=\frac{20}{15}+\frac{72}{15}$$

Tā te mea he rite te tauraro o \frac{20}{15} me \frac{72}{15}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{46}{15}r=\frac{20+72}{15}$$

Tāpirihia te 20 ki te 72, ka 92.

$$\frac{46}{15}r=\frac{92}{15}$$

Me whakarea ngā taha e rua ki te \frac{15}{46}, te tau utu o \frac{46}{15}.

$$r=\frac{92}{15}\times \frac{15}{46}$$

Me whakarea te \frac{92}{15} ki te \frac{15}{46} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$r=\frac{92\times 15}{15\times 46}$$

Me whakakore tahi te 15 i te taurunga me te tauraro.

$$r=\frac{92}{46}$$

Whakawehea te 92 ki te 46, kia riro ko 2.

$$r=2$$