Whakaoti i te 1/4(x-2)=1/3(2x+6)

$$\frac { 1 } { 4 } ( x - 2 ) = \frac { 1 } { 3 } ( 2 x + 6 )$$

Whakaoti mō x

$$x=-6$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te x-2.

$$\frac{1}{4}x+\frac{1}{4}\left(-2\right)=\frac{1}{3}\left(2x+6\right)$$

Whakareatia te \frac{1}{4} ki te -2, ka \frac{-2}{4}.

$$\frac{1}{4}x+\frac{-2}{4}=\frac{1}{3}\left(2x+6\right)$$

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

$$\frac{1}{4}x-\frac{1}{2}=\frac{1}{3}\left(2x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{3} ki te 2x+6.

$$\frac{1}{4}x-\frac{1}{2}=\frac{1}{3}\times 2x+\frac{1}{3}\times 6$$

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

$$\frac{1}{4}x-\frac{1}{2}=\frac{2}{3}x+\frac{1}{3}\times 6$$

Whakareatia te \frac{1}{3} ki te 6, ka \frac{6}{3}.

$$\frac{1}{4}x-\frac{1}{2}=\frac{2}{3}x+\frac{6}{3}$$

Whakawehea te 6 ki te 3, kia riro ko 2.

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

Tangohia te \frac{2}{3}x mai i ngā taha e rua.

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

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

$$-\frac{5}{12}x-\frac{1}{2}=2$$

Me tāpiri te \frac{1}{2} ki ngā taha e rua.

$$-\frac{5}{12}x=2+\frac{1}{2}$$

Me tahuri te 2 ki te hautau \frac{4}{2}.

$$-\frac{5}{12}x=\frac{4}{2}+\frac{1}{2}$$

Tā te mea he rite te tauraro o \frac{4}{2} me \frac{1}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$-\frac{5}{12}x=\frac{4+1}{2}$$

Tāpirihia te 4 ki te 1, ka 5.

$$-\frac{5}{12}x=\frac{5}{2}$$

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

$$x=\frac{5}{2}\left(-\frac{12}{5}\right)$$

Me whakarea te \frac{5}{2} ki te -\frac{12}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{5\left(-12\right)}{2\times 5}$$

Me whakakore tahi te 5 i te taurunga me te tauraro.

$$x=\frac{-12}{2}$$

Whakawehea te -12 ki te 2, kia riro ko -6.

$$x=-6$$