Whakaoti i te x-2/3+x-5/4=x-5/6+x-7/8

$$\frac { x - 2 } { 3 } + \frac { x - 5 } { 4 } = \frac { x - 5 } { 6 } + \frac { x - 7 } { 8 }$$

Whakaoti mō x

$$x=\frac{5}{7}\approx 0.714285714$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 24, arā, te tauraro pātahi he tino iti rawa te kitea o 3,4,6,8.

$$8\left(x-2\right)+6\left(x-5\right)=4\left(x-5\right)+3\left(x-7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8 ki te x-2.

$$8x-16+6\left(x-5\right)=4\left(x-5\right)+3\left(x-7\right)$$

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

$$8x-16+6x-30=4\left(x-5\right)+3\left(x-7\right)$$

Pahekotia te 8x me 6x, ka 14x.

$$14x-16-30=4\left(x-5\right)+3\left(x-7\right)$$

Tangohia te 30 i te -16, ka -46.

$$14x-46=4\left(x-5\right)+3\left(x-7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-5.

$$14x-46=4x-20+3\left(x-7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x-7.

$$14x-46=4x-20+3x-21$$

Pahekotia te 4x me 3x, ka 7x.

$$14x-46=7x-20-21$$

Tangohia te 21 i te -20, ka -41.

$$14x-46=7x-41$$

Tangohia te 7x mai i ngā taha e rua.

$$14x-46-7x=-41$$

Pahekotia te 14x me -7x, ka 7x.

$$7x-46=-41$$

Me tāpiri te 46 ki ngā taha e rua.

$$7x=-41+46$$

Tāpirihia te -41 ki te 46, ka 5.

$$7x=5$$

Whakawehea ngā taha e rua ki te 7.

$$x=\frac{5}{7}$$