Whakaoti i te 2x-(2x-3x-1/8)=2/3(x+2/6)-1/4

$$2 x - ( 2 x - \frac { 3 x - 1 } { 8 } ) = \frac { 2 } { 3 } ( \frac { x + 2 } { 6 } ) - \frac { 1 } { 4 }$$

Whakaoti mō x

$$x=\frac{7}{19}\approx 0.368421053$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 24, arā, te tauraro pātahi he tino iti rawa te kitea o 8,3,6,4.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}\left(x+2\right)-6$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{8}{3} ki te x+2.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{8}{3}\times 2-6$$

Tuhia te \frac{8}{3}\times 2 hei hautanga kotahi.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{8\times 2}{3}-6$$

Whakareatia te 8 ki te 2, ka 16.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16}{3}-6$$

Me tahuri te 6 ki te hautau \frac{18}{3}.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16}{3}-\frac{18}{3}$$

Tā te mea he rite te tauraro o \frac{16}{3} me \frac{18}{3}, me tango rāua mā te tango i ō raua taurunga.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16-18}{3}$$

Tangohia te 18 i te 16, ka -2.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x-\frac{2}{3}$$

Whakawehea ia wā o 3x-1 ki te 8, kia riro ko \frac{3}{8}x-\frac{1}{8}.

$$48x-24\left(2x-\left(\frac{3}{8}x-\frac{1}{8}\right)\right)=\frac{8}{3}x-\frac{2}{3}$$

Hei kimi i te tauaro o \frac{3}{8}x-\frac{1}{8}, kimihia te tauaro o ia taurangi.

$$48x-24\left(2x-\frac{3}{8}x-\left(-\frac{1}{8}\right)\right)=\frac{8}{3}x-\frac{2}{3}$$

Ko te tauaro o -\frac{1}{8} ko \frac{1}{8}.

$$48x-24\left(2x-\frac{3}{8}x+\frac{1}{8}\right)=\frac{8}{3}x-\frac{2}{3}$$

Pahekotia te 2x me -\frac{3}{8}x, ka \frac{13}{8}x.

$$48x-24\left(\frac{13}{8}x+\frac{1}{8}\right)=\frac{8}{3}x-\frac{2}{3}$$

Whakamahia te āhuatanga tohatoha hei whakarea te -24 ki te \frac{13}{8}x+\frac{1}{8}.

$$48x-24\times \frac{13}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}$$

Tuhia te -24\times \frac{13}{8} hei hautanga kotahi.

$$48x+\frac{-24\times 13}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}$$

Whakareatia te -24 ki te 13, ka -312.

$$48x+\frac{-312}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}$$

Whakawehea te -312 ki te 8, kia riro ko -39.

$$48x-39x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}$$

Whakareatia te -24 ki te \frac{1}{8}, ka \frac{-24}{8}.

$$48x-39x+\frac{-24}{8}=\frac{8}{3}x-\frac{2}{3}$$

Whakawehea te -24 ki te 8, kia riro ko -3.

$$48x-39x-3=\frac{8}{3}x-\frac{2}{3}$$

Pahekotia te 48x me -39x, ka 9x.

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

Tangohia te \frac{8}{3}x mai i ngā taha e rua.

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

Pahekotia te 9x me -\frac{8}{3}x, ka \frac{19}{3}x.

$$\frac{19}{3}x-3=-\frac{2}{3}$$

Me tāpiri te 3 ki ngā taha e rua.

$$\frac{19}{3}x=-\frac{2}{3}+3$$

Me tahuri te 3 ki te hautau \frac{9}{3}.

$$\frac{19}{3}x=-\frac{2}{3}+\frac{9}{3}$$

Tā te mea he rite te tauraro o -\frac{2}{3} me \frac{9}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{19}{3}x=\frac{-2+9}{3}$$

Tāpirihia te -2 ki te 9, ka 7.

$$\frac{19}{3}x=\frac{7}{3}$$

Me whakarea ngā taha e rua ki te \frac{3}{19}, te tau utu o \frac{19}{3}.

$$x=\frac{7}{3}\times \frac{3}{19}$$

Me whakarea te \frac{7}{3} ki te \frac{3}{19} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{7\times 3}{3\times 19}$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$x=\frac{7}{19}$$