Whakaoti i te {l}{x-5/12-3x+1/6=4x-3/3-5x+1/4}{y=x+4-x-1x+3*15}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { \frac{x - 5}{12} - \frac{3 x + 1}{6} = \frac{4 x - 3}{3} - \frac{5 x + 1}{4} }\\ { y = x + 4 - x - 1 x + 3 \cdot 15 }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Whakaoti mō x, y, z, a

$$a = \frac{143}{3} = 47\frac{2}{3} \approx 47.666666667$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 12,6,3,4.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 3x+1.

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

Pahekotia te x me -6x, ka -5x.

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

Tangohia te 2 i te -5, ka -7.

$$-5x-7=4\left(4x-3\right)-3\left(5x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 4x-3.

$$-5x-7=16x-12-3\left(5x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te 5x+1.

$$-5x-7=16x-12-15x-3$$

Pahekotia te 16x me -15x, ka x.

$$-5x-7=x-12-3$$

Tangohia te 3 i te -12, ka -15.

$$-5x-7=x-15$$

Tangohia te x mai i ngā taha e rua.

$$-5x-7-x=-15$$

Pahekotia te -5x me -x, ka -6x.

$$-6x-7=-15$$

Me tāpiri te 7 ki ngā taha e rua.

$$-6x=-15+7$$

Tāpirihia te -15 ki te 7, ka -8.

$$-6x=-8$$

Whakawehea ngā taha e rua ki te -6.

$$x=\frac{-8}{-6}$$

Whakahekea te hautanga \frac{-8}{-6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -2.

$$x=\frac{4}{3}$$

Whakaarohia te whārite tuarua. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$y=\frac{4}{3}+4-\frac{4}{3}-\frac{4}{3}+3\times 15$$

Tāpirihia te \frac{4}{3} ki te 4, ka \frac{16}{3}.

$$y=\frac{16}{3}-\frac{4}{3}-\frac{4}{3}+3\times 15$$

Tangohia te \frac{4}{3} i te \frac{16}{3}, ka 4.

$$y=4-\frac{4}{3}+3\times 15$$

Tangohia te \frac{4}{3} i te 4, ka \frac{8}{3}.

$$y=\frac{8}{3}+3\times 15$$

Whakareatia te 3 ki te 15, ka 45.

$$y=\frac{8}{3}+45$$

Tāpirihia te \frac{8}{3} ki te 45, ka \frac{143}{3}.

$$y=\frac{143}{3}$$

Whakaarohia te whārite tuatoru. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$z=\frac{143}{3}$$

Whakaarohia te whārite tuawhā. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$a=\frac{143}{3}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{4}{3} y=\frac{143}{3} z=\frac{143}{3} a=\frac{143}{3}$$