Whakaoti i te 4(x-2)-5(x-6)=2(x+1)+3(2x+3)

$$4 ( x - 2 ) - 5 ( x - 6 ) = 2 ( x + 1 ) + 3 ( 2 x + 3 )$$

Whakaoti mō x

$$x = \frac{11}{9} = 1\frac{2}{9} \approx 1.222222222$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-2.

$$4x-8-5\left(x-6\right)=2\left(x+1\right)+3\left(2x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te x-6.

$$4x-8-5x+30=2\left(x+1\right)+3\left(2x+3\right)$$

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

$$-x-8+30=2\left(x+1\right)+3\left(2x+3\right)$$

Tāpirihia te -8 ki te 30, ka 22.

$$-x+22=2\left(x+1\right)+3\left(2x+3\right)$$

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

$$-x+22=2x+2+3\left(2x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 2x+3.

$$-x+22=2x+2+6x+9$$

Pahekotia te 2x me 6x, ka 8x.

$$-x+22=8x+2+9$$

Tāpirihia te 2 ki te 9, ka 11.

$$-x+22=8x+11$$

Tangohia te 8x mai i ngā taha e rua.

$$-x+22-8x=11$$

Pahekotia te -x me -8x, ka -9x.

$$-9x+22=11$$

Tangohia te 22 mai i ngā taha e rua.

$$-9x=11-22$$

Tangohia te 22 i te 11, ka -11.

$$-9x=-11$$

Whakawehea ngā taha e rua ki te -9.

$$x=\frac{-11}{-9}$$

Ka taea te hautanga \frac{-11}{-9} te whakamāmā ki te \frac{11}{9} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{11}{9}$$