Whakaoti i te 2/5[x-5/3(x+4)]=x-3/3-2/3(x+2)

$$\frac { 2 } { 5 } [ x - \frac { 5 } { 3 } ( x + 4 ) ] = \frac { x - 3 } { 3 } - \frac { 2 } { 3 } ( x + 2 )$$

Whakaoti mō x

$$x=5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 15, arā, te tauraro pātahi he tino iti rawa te kitea o 5,3.

$$6\left(x-\frac{5}{3}\left(x+4\right)\right)=5\left(x-3\right)-10\left(x+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{5}{3} ki te x+4.

$$6\left(x-\frac{5}{3}x-\frac{5}{3}\times 4\right)=5\left(x-3\right)-10\left(x+2\right)$$

Tuhia te -\frac{5}{3}\times 4 hei hautanga kotahi.

$$6\left(x-\frac{5}{3}x+\frac{-5\times 4}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Whakareatia te -5 ki te 4, ka -20.

$$6\left(x-\frac{5}{3}x+\frac{-20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Ka taea te hautanga \frac{-20}{3} te tuhi anō ko -\frac{20}{3} mā te tango i te tohu tōraro.

$$6\left(x-\frac{5}{3}x-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Pahekotia te x me -\frac{5}{3}x, ka -\frac{2}{3}x.

$$6\left(-\frac{2}{3}x-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te -\frac{2}{3}x-\frac{20}{3}.

$$6\left(-\frac{2}{3}\right)x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Tuhia te 6\left(-\frac{2}{3}\right) hei hautanga kotahi.

$$\frac{6\left(-2\right)}{3}x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Whakareatia te 6 ki te -2, ka -12.

$$\frac{-12}{3}x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Whakawehea te -12 ki te 3, kia riro ko -4.

$$-4x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Tuhia te 6\left(-\frac{20}{3}\right) hei hautanga kotahi.

$$-4x+\frac{6\left(-20\right)}{3}=5\left(x-3\right)-10\left(x+2\right)$$

Whakareatia te 6 ki te -20, ka -120.

$$-4x+\frac{-120}{3}=5\left(x-3\right)-10\left(x+2\right)$$

Whakawehea te -120 ki te 3, kia riro ko -40.

$$-4x-40=5\left(x-3\right)-10\left(x+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x-3.

$$-4x-40=5x-15-10\left(x+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -10 ki te x+2.

$$-4x-40=5x-15-10x-20$$

Pahekotia te 5x me -10x, ka -5x.

$$-4x-40=-5x-15-20$$

Tangohia te 20 i te -15, ka -35.

$$-4x-40=-5x-35$$

Me tāpiri te 5x ki ngā taha e rua.

$$-4x-40+5x=-35$$

Pahekotia te -4x me 5x, ka x.

$$x-40=-35$$

Me tāpiri te 40 ki ngā taha e rua.

$$x=-35+40$$

Tāpirihia te -35 ki te 40, ka 5.

$$x=5$$