Whakaoti i te 9x-1<3/4(16x-2)

$$9 x - 1 < \frac { 3 } { 4 } ( 16 x - 2 )$$

Whakaoti mō x

$$x>\frac{1}{6}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4} ki te 16x-2.

$$9x-1<\frac{3}{4}\times 16x+\frac{3}{4}\left(-2\right)$$

Tuhia te \frac{3}{4}\times 16 hei hautanga kotahi.

$$9x-1<\frac{3\times 16}{4}x+\frac{3}{4}\left(-2\right)$$

Whakareatia te 3 ki te 16, ka 48.

$$9x-1<\frac{48}{4}x+\frac{3}{4}\left(-2\right)$$

Whakawehea te 48 ki te 4, kia riro ko 12.

$$9x-1<12x+\frac{3}{4}\left(-2\right)$$

Tuhia te \frac{3}{4}\left(-2\right) hei hautanga kotahi.

$$9x-1<12x+\frac{3\left(-2\right)}{4}$$

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

$$9x-1<12x+\frac{-6}{4}$$

Whakahekea te hautanga \frac{-6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$9x-1<12x-\frac{3}{2}$$

Tangohia te 12x mai i ngā taha e rua.

$$9x-1-12x<-\frac{3}{2}$$

Pahekotia te 9x me -12x, ka -3x.

$$-3x-1<-\frac{3}{2}$$

Me tāpiri te 1 ki ngā taha e rua.

$$-3x<-\frac{3}{2}+1$$

Me tahuri te 1 ki te hautau \frac{2}{2}.

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

Tā te mea he rite te tauraro o -\frac{3}{2} me \frac{2}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te -3 ki te 2, ka -1.

$$-3x<-\frac{1}{2}$$

Whakawehea ngā taha e rua ki te -3. I te mea he tōraro a -3, ka huri te ahunga koreōrite.

$$x>\frac{-\frac{1}{2}}{-3}$$

Tuhia te \frac{-\frac{1}{2}}{-3} hei hautanga kotahi.

$$x>\frac{-1}{2\left(-3\right)}$$

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

$$x>\frac{-1}{-6}$$

Ka taea te hautanga \frac{-1}{-6} te whakamāmā ki te \frac{1}{6} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x>\frac{1}{6}$$