Whakaoti i te (m)x-4/8+x+1/2=x+7/2-x-5/8-frac{x+6}{4}

$$( m ) \frac { x - 4 } { 8 } + \frac { x + 1 } { 2 } = \frac { x + 7 } { 2 } - \frac { x - 5 } { 8 } - \frac { x + 6 } { 4 }$$

Whakaoti mō m

$$m=-\frac{3x-17}{x-4}$$

$$x\neq 4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 8, arā, te tauraro pātahi he tino iti rawa te kitea o 8,2,4.

$$m\left(x-4\right)+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

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

$$mx-4m+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

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

$$mx-4m+4x+4=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+7.

$$mx-4m+4x+4=4x+28-\left(x-5\right)-2\left(x+6\right)$$

Hei kimi i te tauaro o x-5, kimihia te tauaro o ia taurangi.

$$mx-4m+4x+4=4x+28-x+5-2\left(x+6\right)$$

Pahekotia te 4x me -x, ka 3x.

$$mx-4m+4x+4=3x+28+5-2\left(x+6\right)$$

Tāpirihia te 28 ki te 5, ka 33.

$$mx-4m+4x+4=3x+33-2\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x+6.

$$mx-4m+4x+4=3x+33-2x-12$$

Pahekotia te 3x me -2x, ka x.

$$mx-4m+4x+4=x+33-12$$

Tangohia te 12 i te 33, ka 21.

$$mx-4m+4x+4=x+21$$

Tangohia te 4x mai i ngā taha e rua.

$$mx-4m+4=x+21-4x$$

Pahekotia te x me -4x, ka -3x.

$$mx-4m+4=-3x+21$$

Tangohia te 4 mai i ngā taha e rua.

$$mx-4m=-3x+21-4$$

Tangohia te 4 i te 21, ka 17.

$$mx-4m=-3x+17$$

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

$$\left(x-4\right)m=-3x+17$$

He hanga arowhānui tō te whārite.

$$\left(x-4\right)m=17-3x$$

Whakawehea ngā taha e rua ki te x-4.

$$\frac{\left(x-4\right)m}{x-4}=\frac{17-3x}{x-4}$$

Mā te whakawehe ki te x-4 ka wetekia te whakareanga ki te x-4.

$$m=\frac{17-3x}{x-4}$$

Whakaoti mō x

$$x=\frac{4m+17}{m+3}$$

$$m\neq -3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 8, arā, te tauraro pātahi he tino iti rawa te kitea o 8,2,4.

$$m\left(x-4\right)+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

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

$$mx-4m+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

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

$$mx-4m+4x+4=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+7.

$$mx-4m+4x+4=4x+28-\left(x-5\right)-2\left(x+6\right)$$

Hei kimi i te tauaro o x-5, kimihia te tauaro o ia taurangi.

$$mx-4m+4x+4=4x+28-x+5-2\left(x+6\right)$$

Pahekotia te 4x me -x, ka 3x.

$$mx-4m+4x+4=3x+28+5-2\left(x+6\right)$$

Tāpirihia te 28 ki te 5, ka 33.

$$mx-4m+4x+4=3x+33-2\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x+6.

$$mx-4m+4x+4=3x+33-2x-12$$

Pahekotia te 3x me -2x, ka x.

$$mx-4m+4x+4=x+33-12$$

Tangohia te 12 i te 33, ka 21.

$$mx-4m+4x+4=x+21$$

Tangohia te x mai i ngā taha e rua.

$$mx-4m+4x+4-x=21$$

Pahekotia te 4x me -x, ka 3x.

$$mx-4m+3x+4=21$$

Me tāpiri te 4m ki ngā taha e rua.

$$mx+3x+4=21+4m$$

Tangohia te 4 mai i ngā taha e rua.

$$mx+3x=21+4m-4$$

Tangohia te 4 i te 21, ka 17.

$$mx+3x=17+4m$$

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

$$\left(m+3\right)x=17+4m$$

He hanga arowhānui tō te whārite.

$$\left(m+3\right)x=4m+17$$

Whakawehea ngā taha e rua ki te m+3.

$$\frac{\left(m+3\right)x}{m+3}=\frac{4m+17}{m+3}$$

Mā te whakawehe ki te m+3 ka wetekia te whakareanga ki te m+3.

$$x=\frac{4m+17}{m+3}$$