Whakaoti i te 3/2(x-2)<3/4(x-8)

$$\frac{ 3 }{ 2 } (x-2) < \frac{ 3 }{ 4 } (x-8)$$

Whakaoti mō x

$$x<-4$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{2} ki te x-2.

$$\frac{3}{2}x+\frac{3}{2}\left(-2\right)<\frac{3}{4}\left(x-8\right)$$

Tuhia te \frac{3}{2}\left(-2\right) hei hautanga kotahi.

$$\frac{3}{2}x+\frac{3\left(-2\right)}{2}<\frac{3}{4}\left(x-8\right)$$

Whakareatia te 3 ki te -2, ka -6.

$$\frac{3}{2}x+\frac{-6}{2}<\frac{3}{4}\left(x-8\right)$$

Whakawehea te -6 ki te 2, kia riro ko -3.

$$\frac{3}{2}x-3<\frac{3}{4}\left(x-8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4} ki te x-8.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{3}{4}\left(-8\right)$$

Tuhia te \frac{3}{4}\left(-8\right) hei hautanga kotahi.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{3\left(-8\right)}{4}$$

Whakareatia te 3 ki te -8, ka -24.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{-24}{4}$$

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

$$\frac{3}{2}x-3<\frac{3}{4}x-6$$

Tangohia te \frac{3}{4}x mai i ngā taha e rua.

$$\frac{3}{2}x-3-\frac{3}{4}x<-6$$

Pahekotia te \frac{3}{2}x me -\frac{3}{4}x, ka \frac{3}{4}x.

$$\frac{3}{4}x-3<-6$$

Me tāpiri te 3 ki ngā taha e rua.

$$\frac{3}{4}x<-6+3$$

Tāpirihia te -6 ki te 3, ka -3.

$$\frac{3}{4}x<-3$$

Me whakarea ngā taha e rua ki te \frac{4}{3}, te tau utu o \frac{3}{4}. I te mea he tōrunga te \frac{3}{4}, kāore e huri te ahunga koreōrite.

$$x<-3\times \frac{4}{3}$$

Whakareatia -3 ki te \frac{4}{3}.

$$x<-4$$