Whakaoti i te x+1/2*(x-1/2)=2x-1/4(x+2)+15/4

$$\frac { x + 1 } { 2 } \cdot ( x - \frac { 1 } { 2 } ) = \frac { 2 x - 1 } { 4 } ( x + 2 ) + \frac { 15 } { 4 }$$

Whakaoti mō x

$$x=-7$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$2\left(x+1\right)\left(x-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x+1.

$$\left(2x+2\right)\left(x-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x+2 ki ia tau o x-\frac{1}{2}.

$$2x^{2}+2x\left(-\frac{1}{2}\right)+2x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Me whakakore te 2 me te 2.

$$2x^{2}-x+2x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Pahekotia te -x me 2x, ka x.

$$2x^{2}+x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Me whakakore te 2 me te 2.

$$2x^{2}+x-1=\left(2x-1\right)\left(x+2\right)+15$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x-1 ki ia tau o x+2.

$$2x^{2}+x-1=2x^{2}+4x-x-2+15$$

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

$$2x^{2}+x-1=2x^{2}+3x-2+15$$

Tāpirihia te -2 ki te 15, ka 13.

$$2x^{2}+x-1=2x^{2}+3x+13$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$2x^{2}+x-1-2x^{2}=3x+13$$

Pahekotia te 2x^{2} me -2x^{2}, ka 0.

$$x-1=3x+13$$

Tangohia te 3x mai i ngā taha e rua.

$$x-1-3x=13$$

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

$$-2x-1=13$$

Me tāpiri te 1 ki ngā taha e rua.

$$-2x=13+1$$

Tāpirihia te 13 ki te 1, ka 14.

$$-2x=14$$

Whakawehea ngā taha e rua ki te -2.

$$x=\frac{14}{-2}$$

Whakawehea te 14 ki te -2, kia riro ko -7.

$$x=-7$$