Whakaoti i te ax+b/3=cx+d/2

$$\frac { a x + b } { 3 } = \frac { c x + d } { 2 }$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{-3cx+2b-3d}{2x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=\frac{3d}{2}\text{ and }x=0\end{matrix}\right.$$

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.

$$2\left(ax+b\right)=3\left(cx+d\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te ax+b.

$$2ax+2b=3\left(cx+d\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te cx+d.

$$2ax+2b=3cx+3d$$

Tangohia te 2b mai i ngā taha e rua.

$$2ax=3cx+3d-2b$$

He hanga arowhānui tō te whārite.

$$2xa=3cx+3d-2b$$

Whakawehea ngā taha e rua ki te 2x.

$$\frac{2xa}{2x}=\frac{3cx+3d-2b}{2x}$$

Mā te whakawehe ki te 2x ka wetekia te whakareanga ki te 2x.

$$a=\frac{3cx+3d-2b}{2x}$$

Whakaoti mō b

$$b=-ax+\frac{3cx}{2}+\frac{3d}{2}$$

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.

$$2\left(ax+b\right)=3\left(cx+d\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te ax+b.

$$2ax+2b=3\left(cx+d\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te cx+d.

$$2ax+2b=3cx+3d$$

Tangohia te 2ax mai i ngā taha e rua.

$$2b=3cx+3d-2ax$$

He hanga arowhānui tō te whārite.

$$2b=3cx-2ax+3d$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2b}{2}=\frac{3cx-2ax+3d}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$b=\frac{3cx-2ax+3d}{2}$$

Whakawehe 3cx+3d-2ax ki te 2.

$$b=-ax+\frac{3cx}{2}+\frac{3d}{2}$$