Whakaoti i te x-4/8+x+1/2=x+7/2-x-5/8-frac{x+6}{4}

$$\frac { x - 4 } { 8 } + \frac { x + 1 } { 2 } = \frac { x + 7 } { 2 } - \frac { x - 5 } { 8 } - \frac { x + 6 } { 4 }$$

Whakaoti mō x

$$x = \frac{21}{4} = 5\frac{1}{4} = 5.25$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 8, arā, te tauraro pātahi he tino iti rawa te kitea o 8,2,4.

$$x-4+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+1.

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

Pahekotia te x me 4x, ka 5x.

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

Tāpirihia te -4 ki te 4, ka 0.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+7.

$$5x=4x+28-\left(x-5\right)-2\left(x+6\right)$$

Hei kimi i te tauaro o x-5, kimihia te tauaro o ia taurangi.

$$5x=4x+28-x-\left(-5\right)-2\left(x+6\right)$$

Ko te tauaro o -5 ko 5.

$$5x=4x+28-x+5-2\left(x+6\right)$$

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

$$5x=3x+28+5-2\left(x+6\right)$$

Tāpirihia te 28 ki te 5, ka 33.

$$5x=3x+33-2\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x+6.

$$5x=3x+33-2x-12$$

Pahekotia te 3x me -2x, ka x.

$$5x=x+33-12$$

Tangohia te 12 i te 33, ka 21.

$$5x=x+21$$

Tangohia te x mai i ngā taha e rua.

$$5x-x=21$$

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

$$4x=21$$

Whakawehea ngā taha e rua ki te 4.

$$x=\frac{21}{4}$$