Whakaoti i te 4x-1/3-9x-4/7-x/2+10/7=frac{x-5}{6}+frac{2x+3}{14}

$$\frac { 4 x - 1 } { 3 } - \frac { 9 x - 4 } { 7 } - \frac { x } { 2 } + \frac { 10 } { 7 } = \frac { x - 5 } { 6 } + \frac { 2 x + 3 } { 14 }$$

Whakaoti mō x

$$x=3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 42, arā, te tauraro pātahi he tino iti rawa te kitea o 3,7,2,6,14.

$$14\left(4x-1\right)-6\left(9x-4\right)-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 14 ki te 4x-1.

$$56x-14-6\left(9x-4\right)-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te 9x-4.

$$56x-14-54x+24-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

Pahekotia te 56x me -54x, ka 2x.

$$2x-14+24-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

Tāpirihia te -14 ki te 24, ka 10.

$$2x+10-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

Pahekotia te 2x me -21x, ka -19x.

$$-19x+10+60=7\left(x-5\right)+3\left(2x+3\right)$$

Tāpirihia te 10 ki te 60, ka 70.

$$-19x+70=7\left(x-5\right)+3\left(2x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7 ki te x-5.

$$-19x+70=7x-35+3\left(2x+3\right)$$

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

$$-19x+70=7x-35+6x+9$$

Pahekotia te 7x me 6x, ka 13x.

$$-19x+70=13x-35+9$$

Tāpirihia te -35 ki te 9, ka -26.

$$-19x+70=13x-26$$

Tangohia te 13x mai i ngā taha e rua.

$$-19x+70-13x=-26$$

Pahekotia te -19x me -13x, ka -32x.

$$-32x+70=-26$$

Tangohia te 70 mai i ngā taha e rua.

$$-32x=-26-70$$

Tangohia te 70 i te -26, ka -96.

$$-32x=-96$$

Whakawehea ngā taha e rua ki te -32.

$$x=\frac{-96}{-32}$$

Whakawehea te -96 ki te -32, kia riro ko 3.

$$x=3$$