Whakaoti i te 5x/3-x-2/4=9/4-1/2(x-frac{2x-1}{3})

$$\frac{ 5x }{ 3 } - \frac{ x-2 }{ 4 } = \frac{ 9 }{ 4 } - \frac{ 1 }{ 2 } (x- \frac{ 2x-1 }{ 3 } )$$

Whakaoti mō x

$$x=1$$

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 3,4,2.

$$4\times 5x-3\left(x-2\right)=27-6\left(x-\frac{2x-1}{3}\right)$$

Whakareatia te 4 ki te 5, ka 20.

$$20x-3\left(x-2\right)=27-6\left(x-\frac{2x-1}{3}\right)$$

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

$$20x-3x+6=27-6\left(x-\frac{2x-1}{3}\right)$$

Pahekotia te 20x me -3x, ka 17x.

$$17x+6=27-6\left(x-\frac{2x-1}{3}\right)$$

Whakawehea ia wā o 2x-1 ki te 3, kia riro ko \frac{2}{3}x-\frac{1}{3}.

$$17x+6=27-6\left(x-\left(\frac{2}{3}x-\frac{1}{3}\right)\right)$$

Hei kimi i te tauaro o \frac{2}{3}x-\frac{1}{3}, kimihia te tauaro o ia taurangi.

$$17x+6=27-6\left(x-\frac{2}{3}x-\left(-\frac{1}{3}\right)\right)$$

Ko te tauaro o -\frac{1}{3} ko \frac{1}{3}.

$$17x+6=27-6\left(x-\frac{2}{3}x+\frac{1}{3}\right)$$

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

$$17x+6=27-6\left(\frac{1}{3}x+\frac{1}{3}\right)$$

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

$$17x+6=27-6\times \frac{1}{3}x-6\times \frac{1}{3}$$

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

$$17x+6=27+\frac{-6}{3}x-6\times \frac{1}{3}$$

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

$$17x+6=27-2x-6\times \frac{1}{3}$$

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

$$17x+6=27-2x+\frac{-6}{3}$$

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

$$17x+6=27-2x-2$$

Tangohia te 2 i te 27, ka 25.

$$17x+6=25-2x$$

Me tāpiri te 2x ki ngā taha e rua.

$$17x+6+2x=25$$

Pahekotia te 17x me 2x, ka 19x.

$$19x+6=25$$

Tangohia te 6 mai i ngā taha e rua.

$$19x=25-6$$

Tangohia te 6 i te 25, ka 19.

$$19x=19$$

Whakawehea ngā taha e rua ki te 19.

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

Whakawehea te 19 ki te 19, kia riro ko 1.

$$x=1$$