Whakaoti i te 7/6>4x+2/x-7

$$\frac { 7 } { 6 } > \frac { 4 x + 2 } { x - 7 }$$

Whakaoti mō x

$$x\in \left(-\frac{61}{17},7\right)$$

Ngā Upane Otinga

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa. Ka huri tēnei i te aronga o te tohu.

$$\frac{4x+2}{x-7}<\frac{7}{6}$$

Kāore e taea a te tauraro x-7 te numa kore nā te mea kāore te rituatanga mā te kore e tautuhi. E rua ngā kēhi.

$$x-7>0 x-7<0$$

Whakaarohia te kēhi i ngā wā kei te tōrunga a x-7. Neke atu a -7 ki te taha matau.

$$x>7$$

Kāore te tōrite tuatahi e whakarerekē te aronga ina e whakarea ana mā x-7 mō x-7>0.

$$4x+2<\frac{7}{6}\left(x-7\right)$$

Whakarea te katoa o te taha matau.

$$4x+2<\frac{7}{6}x-\frac{49}{6}$$

Neke atu ngā kīanga tau e whai ana i x ki te taha mauī me ētahi atu kupu katoa ki te taha matau.

$$4x-\frac{7}{6}x<-2-\frac{49}{6}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{17}{6}x<-\frac{61}{6}$$

Whakawehea ngā taha e rua ki te \frac{17}{6}. I te mea he tōrunga te \frac{17}{6}, kāore e huri te ahunga koreōrite.

$$x<-\frac{61}{17}$$

Whakaarohia te herenga x>7 e tautuhi ana ki runga.

$$x\in \emptyset$$

Tēnā, me whakaarohia te tauira ina e tōraro a x-7. Neke atu a -7 ki te taha matau.

$$x<7$$

E whakarerekē ana te aronga o te tōrite tuatahi hei ngā wā e whakarea ana a x-7 mō x-7<0.

$$4x+2>\frac{7}{6}\left(x-7\right)$$

Whakarea te katoa o te taha matau.

$$4x+2>\frac{7}{6}x-\frac{49}{6}$$

Neke atu ngā kīanga tau e whai ana i x ki te taha mauī me ētahi atu kupu katoa ki te taha matau.

$$4x-\frac{7}{6}x>-2-\frac{49}{6}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{17}{6}x>-\frac{61}{6}$$

Whakawehea ngā taha e rua ki te \frac{17}{6}. I te mea he tōrunga te \frac{17}{6}, kāore e huri te ahunga koreōrite.

$$x>-\frac{61}{17}$$

Whakaarohia te herenga x<7 e tautuhi ana ki runga.

$$x\in \left(-\frac{61}{17},7\right)$$

Ko te otinga whakamutunga ko te whakakotahi i ngā otinga kua whiwhi.

$$x\in \left(-\frac{61}{17},7\right)$$