Whakaoti i te 3/4(z+8)=1/3(z-12)

$$\frac { 3 } { 4 } ( z + 8 ) = \frac { 1 } { 3 } ( z - 12 )$$

Whakaoti mō z

$$z=-24$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4} ki te z+8.

$$\frac{3}{4}z+\frac{3}{4}\times 8=\frac{1}{3}\left(z-12\right)$$

Tuhia te \frac{3}{4}\times 8 hei hautanga kotahi.

$$\frac{3}{4}z+\frac{3\times 8}{4}=\frac{1}{3}\left(z-12\right)$$

Whakareatia te 3 ki te 8, ka 24.

$$\frac{3}{4}z+\frac{24}{4}=\frac{1}{3}\left(z-12\right)$$

Whakawehea te 24 ki te 4, kia riro ko 6.

$$\frac{3}{4}z+6=\frac{1}{3}\left(z-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{3} ki te z-12.

$$\frac{3}{4}z+6=\frac{1}{3}z+\frac{1}{3}\left(-12\right)$$

Whakareatia te \frac{1}{3} ki te -12, ka \frac{-12}{3}.

$$\frac{3}{4}z+6=\frac{1}{3}z+\frac{-12}{3}$$

Whakawehea te -12 ki te 3, kia riro ko -4.

$$\frac{3}{4}z+6=\frac{1}{3}z-4$$

Tangohia te \frac{1}{3}z mai i ngā taha e rua.

$$\frac{3}{4}z+6-\frac{1}{3}z=-4$$

Pahekotia te \frac{3}{4}z me -\frac{1}{3}z, ka \frac{5}{12}z.

$$\frac{5}{12}z+6=-4$$

Tangohia te 6 mai i ngā taha e rua.

$$\frac{5}{12}z=-4-6$$

Tangohia te 6 i te -4, ka -10.

$$\frac{5}{12}z=-10$$

Me whakarea ngā taha e rua ki te \frac{12}{5}, te tau utu o \frac{5}{12}.

$$z=-10\times \frac{12}{5}$$

Tuhia te -10\times \frac{12}{5} hei hautanga kotahi.

$$z=\frac{-10\times 12}{5}$$

Whakareatia te -10 ki te 12, ka -120.

$$z=\frac{-120}{5}$$

Whakawehea te -120 ki te 5, kia riro ko -24.

$$z=-24$$