Whakaoti i te 2/3left(left(2x-1right)left(x-4right)+3left(x-1/3right)left(1/3+xright)right)=2/3left(5x^2-xright)+frac{14}{9}

$$\frac{ 2 }{ 3 } \left( \left( 2x-1 \right) \left( x-4 \right) +3 \left( x- \frac{ 1 }{ 3 } \right) \left( \frac{ 1 }{ 3 } +x \right) \right) = \frac{ 2 }{ 3 } \left( 5 { x }^{ 2 } -x \right) + \frac{ 14 }{ 9 }$$

Whakaoti mō x

$$x=\frac{1}{6}\approx 0.166666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-1 ki te x-4 ka whakakotahi i ngā kupu rite.

$$\frac{2}{3}\left(2x^{2}-9x+4+3\left(x-\frac{1}{3}\right)\left(\frac{1}{3}+x\right)\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x-\frac{1}{3}.

$$\frac{2}{3}\left(2x^{2}-9x+4+\left(3x-1\right)\left(\frac{1}{3}+x\right)\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-1 ki te \frac{1}{3}+x ka whakakotahi i ngā kupu rite.

$$\frac{2}{3}\left(2x^{2}-9x+4+3x^{2}-\frac{1}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Pahekotia te 2x^{2} me 3x^{2}, ka 5x^{2}.

$$\frac{2}{3}\left(5x^{2}-9x+4-\frac{1}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Tangohia te \frac{1}{3} i te 4, ka \frac{11}{3}.

$$\frac{2}{3}\left(5x^{2}-9x+\frac{11}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{2}{3} ki te 5x^{2}-9x+\frac{11}{3}.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{2}{3} ki te 5x^{2}-x.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}=\frac{10}{3}x^{2}-\frac{2}{3}x+\frac{14}{9}$$

Tangohia te \frac{10}{3}x^{2} mai i ngā taha e rua.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}-\frac{10}{3}x^{2}=-\frac{2}{3}x+\frac{14}{9}$$

Pahekotia te \frac{10}{3}x^{2} me -\frac{10}{3}x^{2}, ka 0.

$$-6x+\frac{22}{9}=-\frac{2}{3}x+\frac{14}{9}$$

Me tāpiri te \frac{2}{3}x ki ngā taha e rua.

$$-6x+\frac{22}{9}+\frac{2}{3}x=\frac{14}{9}$$

Pahekotia te -6x me \frac{2}{3}x, ka -\frac{16}{3}x.

$$-\frac{16}{3}x+\frac{22}{9}=\frac{14}{9}$$

Tangohia te \frac{22}{9} mai i ngā taha e rua.

$$-\frac{16}{3}x=\frac{14}{9}-\frac{22}{9}$$

Tangohia te \frac{22}{9} i te \frac{14}{9}, ka -\frac{8}{9}.

$$-\frac{16}{3}x=-\frac{8}{9}$$

Me whakarea ngā taha e rua ki te -\frac{3}{16}, te tau utu o -\frac{16}{3}.

$$x=-\frac{8}{9}\left(-\frac{3}{16}\right)$$

Whakareatia te -\frac{8}{9} ki te -\frac{3}{16}, ka \frac{1}{6}.

$$x=\frac{1}{6}$$