Whakaoti i te 2/3(x-2)=1/4*(x-5)

$$\frac { 2 } { 3 } ( x - 2 ) = \frac { 1 } { 4 } \cdot ( x - 5 )$$

Whakaoti mō x

$$x=\frac{1}{5}=0.2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Tuhia te \frac{2}{3}\left(-2\right) hei hautanga kotahi.

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

Whakareatia te 2 ki te -2, ka -4.

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

Ka taea te hautanga \frac{-4}{3} te tuhi anō ko -\frac{4}{3} mā te tango i te tohu tōraro.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te x-5.

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

Whakareatia te \frac{1}{4} ki te -5, ka \frac{-5}{4}.

$$\frac{2}{3}x-\frac{4}{3}=\frac{1}{4}x+\frac{-5}{4}$$

Ka taea te hautanga \frac{-5}{4} te tuhi anō ko -\frac{5}{4} mā te tango i te tohu tōraro.

$$\frac{2}{3}x-\frac{4}{3}=\frac{1}{4}x-\frac{5}{4}$$

Tangohia te \frac{1}{4}x mai i ngā taha e rua.

$$\frac{2}{3}x-\frac{4}{3}-\frac{1}{4}x=-\frac{5}{4}$$

Pahekotia te \frac{2}{3}x me -\frac{1}{4}x, ka \frac{5}{12}x.

$$\frac{5}{12}x-\frac{4}{3}=-\frac{5}{4}$$

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

$$\frac{5}{12}x=-\frac{5}{4}+\frac{4}{3}$$

Ko te maha noa iti rawa atu o 4 me 3 ko 12. Me tahuri -\frac{5}{4} me \frac{4}{3} ki te hautau me te tautūnga 12.

$$\frac{5}{12}x=-\frac{15}{12}+\frac{16}{12}$$

Tā te mea he rite te tauraro o -\frac{15}{12} me \frac{16}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5}{12}x=\frac{-15+16}{12}$$

Tāpirihia te -15 ki te 16, ka 1.

$$\frac{5}{12}x=\frac{1}{12}$$

Me whakarea ngā taha e rua ki te \frac{12}{5}, te tau utu o \frac{5}{12}.

$$x=\frac{1}{12}\times \frac{12}{5}$$

Me whakarea te \frac{1}{12} ki te \frac{12}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{1\times 12}{12\times 5}$$

Me whakakore tahi te 12 i te taurunga me te tauraro.

$$x=\frac{1}{5}$$