Whakaoti i te 4x-1/6-3/2(1/4-x/6)=frac{x}{3}-frac{2}{3}

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

Whakaoti mō x

$$x=-\frac{3}{14}\approx -0.214285714$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 6,2,4,3.

$$2\left(4x-1\right)-18\left(\frac{1}{4}-\frac{x}{6}\right)=4x-8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 4x-1.

$$8x-2-18\left(\frac{1}{4}-\frac{x}{6}\right)=4x-8$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 4 me 6 ko 12. Whakareatia \frac{1}{4} ki te \frac{3}{3}. Whakareatia \frac{x}{6} ki te \frac{2}{2}.

$$8x-2-18\left(\frac{3}{12}-\frac{2x}{12}\right)=4x-8$$

Tā te mea he rite te tauraro o \frac{3}{12} me \frac{2x}{12}, me tango rāua mā te tango i ō raua taurunga.

$$8x-2-18\times \frac{3-2x}{12}=4x-8$$

Tuhia te 18\times \frac{3-2x}{12} hei hautanga kotahi.

$$8x-2-\frac{18\left(3-2x\right)}{12}=4x-8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 18 ki te 3-2x.

$$8x-2-\frac{54-36x}{12}=4x-8$$

Whakawehea ia wā o 54-36x ki te 12, kia riro ko \frac{9}{2}-3x.

$$8x-2-\left(\frac{9}{2}-3x\right)=4x-8$$

Hei kimi i te tauaro o \frac{9}{2}-3x, kimihia te tauaro o ia taurangi.

$$8x-2-\frac{9}{2}-\left(-3x\right)=4x-8$$

Ko te tauaro o -3x ko 3x.

$$8x-2-\frac{9}{2}+3x=4x-8$$

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

$$8x-\frac{4}{2}-\frac{9}{2}+3x=4x-8$$

Tā te mea he rite te tauraro o -\frac{4}{2} me \frac{9}{2}, me tango rāua mā te tango i ō raua taurunga.

$$8x+\frac{-4-9}{2}+3x=4x-8$$

Tangohia te 9 i te -4, ka -13.

$$8x-\frac{13}{2}+3x=4x-8$$

Pahekotia te 8x me 3x, ka 11x.

$$11x-\frac{13}{2}=4x-8$$

Tangohia te 4x mai i ngā taha e rua.

$$11x-\frac{13}{2}-4x=-8$$

Pahekotia te 11x me -4x, ka 7x.

$$7x-\frac{13}{2}=-8$$

Me tāpiri te \frac{13}{2} ki ngā taha e rua.

$$7x=-8+\frac{13}{2}$$

Me tahuri te -8 ki te hautau -\frac{16}{2}.

$$7x=-\frac{16}{2}+\frac{13}{2}$$

Tā te mea he rite te tauraro o -\frac{16}{2} me \frac{13}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$7x=\frac{-16+13}{2}$$

Tāpirihia te -16 ki te 13, ka -3.

$$7x=-\frac{3}{2}$$

Whakawehea ngā taha e rua ki te 7.

$$x=\frac{-\frac{3}{2}}{7}$$

Tuhia te \frac{-\frac{3}{2}}{7} hei hautanga kotahi.

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

Whakareatia te 2 ki te 7, ka 14.

$$x=\frac{-3}{14}$$

Ka taea te hautanga \frac{-3}{14} te tuhi anō ko -\frac{3}{14} mā te tango i te tohu tōraro.

$$x=-\frac{3}{14}$$