Whakaoti i te mx/5-x-1/2=m-2

$$\frac{ mx }{ 5 } - \frac{ x-1 }{ 2 } = m-2$$

Whakaoti mō m (complex solution)

$$\left\{\begin{matrix}\\m=\frac{5}{2}=2.5\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&x=5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 10, arā, te tauraro pātahi he tino iti rawa te kitea o 5,2.

$$2mx-5\left(x-1\right)=10m-20$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te x-1.

$$2mx-5x+5=10m-20$$

Tangohia te 10m mai i ngā taha e rua.

$$2mx-5x+5-10m=-20$$

Me tāpiri te 5x ki ngā taha e rua.

$$2mx+5-10m=-20+5x$$

Tangohia te 5 mai i ngā taha e rua.

$$2mx-10m=-20+5x-5$$

Tangohia te 5 i te -20, ka -25.

$$2mx-10m=-25+5x$$

Pahekotia ngā kīanga tau katoa e whai ana i te m.

$$\left(2x-10\right)m=-25+5x$$

He hanga arowhānui tō te whārite.

$$\left(2x-10\right)m=5x-25$$

Whakawehea ngā taha e rua ki te 2x-10.

$$\frac{\left(2x-10\right)m}{2x-10}=\frac{5x-25}{2x-10}$$

Mā te whakawehe ki te 2x-10 ka wetekia te whakareanga ki te 2x-10.

$$m=\frac{5x-25}{2x-10}$$

Whakawehe -25+5x ki te 2x-10.

$$m=\frac{5}{2}$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}\\x=5\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&m=\frac{5}{2}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 10, arā, te tauraro pātahi he tino iti rawa te kitea o 5,2.

$$2mx-5\left(x-1\right)=10m-20$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te x-1.

$$2mx-5x+5=10m-20$$

Tangohia te 5 mai i ngā taha e rua.

$$2mx-5x=10m-20-5$$

Tangohia te 5 i te -20, ka -25.

$$2mx-5x=10m-25$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(2m-5\right)x=10m-25$$

Whakawehea ngā taha e rua ki te -5+2m.

$$\frac{\left(2m-5\right)x}{2m-5}=\frac{10m-25}{2m-5}$$

Mā te whakawehe ki te -5+2m ka wetekia te whakareanga ki te -5+2m.

$$x=\frac{10m-25}{2m-5}$$

Whakawehe 10m-25 ki te -5+2m.

$$x=5$$

Whakaoti mō m

$$\left\{\begin{matrix}\\m=\frac{5}{2}=2.5\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&x=5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 10, arā, te tauraro pātahi he tino iti rawa te kitea o 5,2.

$$2mx-5\left(x-1\right)=10m-20$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te x-1.

$$2mx-5x+5=10m-20$$

Tangohia te 10m mai i ngā taha e rua.

$$2mx-5x+5-10m=-20$$

Me tāpiri te 5x ki ngā taha e rua.

$$2mx+5-10m=-20+5x$$

Tangohia te 5 mai i ngā taha e rua.

$$2mx-10m=-20+5x-5$$

Tangohia te 5 i te -20, ka -25.

$$2mx-10m=-25+5x$$

Pahekotia ngā kīanga tau katoa e whai ana i te m.

$$\left(2x-10\right)m=-25+5x$$

He hanga arowhānui tō te whārite.

$$\left(2x-10\right)m=5x-25$$

Whakawehea ngā taha e rua ki te 2x-10.

$$\frac{\left(2x-10\right)m}{2x-10}=\frac{5x-25}{2x-10}$$

Mā te whakawehe ki te 2x-10 ka wetekia te whakareanga ki te 2x-10.

$$m=\frac{5x-25}{2x-10}$$

Whakawehe -25+5x ki te 2x-10.

$$m=\frac{5}{2}$$

Whakaoti mō x

$$\left\{\begin{matrix}\\x=5\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&m=\frac{5}{2}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 10, arā, te tauraro pātahi he tino iti rawa te kitea o 5,2.

$$2mx-5\left(x-1\right)=10m-20$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te x-1.

$$2mx-5x+5=10m-20$$

Tangohia te 5 mai i ngā taha e rua.

$$2mx-5x=10m-20-5$$

Tangohia te 5 i te -20, ka -25.

$$2mx-5x=10m-25$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(2m-5\right)x=10m-25$$

Whakawehea ngā taha e rua ki te -5+2m.

$$\frac{\left(2m-5\right)x}{2m-5}=\frac{10m-25}{2m-5}$$

Mā te whakawehe ki te -5+2m ka wetekia te whakareanga ki te -5+2m.

$$x=\frac{10m-25}{2m-5}$$

Whakawehe 10m-25 ki te -5+2m.

$$x=5$$