Whakaoti i te 2/3(4x-1)-[4x-1-3x/2]=x-7/2

$$\frac { 2 } { 3 } ( 4 x - 1 ) - [ 4 x - \frac { 1 - 3 x } { 2 } ] = \frac { x - 7 } { 2 }$$

Whakaoti mō x

$$x=1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$4\left(4x-1\right)-6\left(4x-\frac{1-3x}{2}\right)=3\left(x-7\right)$$

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

$$16x-4-6\left(4x-\frac{1-3x}{2}\right)=3\left(x-7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x-7.

$$16x-4-6\left(4x-\frac{1-3x}{2}\right)=3x-21$$

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

$$16x-4-6\left(4x-\left(\frac{1}{2}-\frac{3}{2}x\right)\right)=3x-21$$

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

$$16x-4-6\left(4x-\frac{1}{2}-\left(-\frac{3}{2}x\right)\right)=3x-21$$

Ko te tauaro o -\frac{3}{2}x ko \frac{3}{2}x.

$$16x-4-6\left(4x-\frac{1}{2}+\frac{3}{2}x\right)=3x-21$$

Pahekotia te 4x me \frac{3}{2}x, ka \frac{11}{2}x.

$$16x-4-6\left(\frac{11}{2}x-\frac{1}{2}\right)=3x-21$$

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te \frac{11}{2}x-\frac{1}{2}.

$$16x-4-6\times \frac{11}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

Tuhia te -6\times \frac{11}{2} hei hautanga kotahi.

$$16x-4+\frac{-6\times 11}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

Whakareatia te -6 ki te 11, ka -66.

$$16x-4+\frac{-66}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

Whakawehea te -66 ki te 2, kia riro ko -33.

$$16x-4-33x-6\left(-\frac{1}{2}\right)=3x-21$$

Tuhia te -6\left(-\frac{1}{2}\right) hei hautanga kotahi.

$$16x-4-33x+\frac{-6\left(-1\right)}{2}=3x-21$$

Whakareatia te -6 ki te -1, ka 6.

$$16x-4-33x+\frac{6}{2}=3x-21$$

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

$$16x-4-33x+3=3x-21$$

Pahekotia te 16x me -33x, ka -17x.

$$-17x-4+3=3x-21$$

Tāpirihia te -4 ki te 3, ka -1.

$$-17x-1=3x-21$$

Tangohia te 3x mai i ngā taha e rua.

$$-17x-1-3x=-21$$

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

$$-20x-1=-21$$

Me tāpiri te 1 ki ngā taha e rua.

$$-20x=-21+1$$

Tāpirihia te -21 ki te 1, ka -20.

$$-20x=-20$$

Whakawehea ngā taha e rua ki te -20.

$$x=\frac{-20}{-20}$$

Whakawehea te -20 ki te -20, kia riro ko 1.

$$x=1$$