Whakaoti i te 2x+3/3x-7>4

$$\frac { 2 x + 3 } { 3 x - 7 } > 4$$

Whakaoti mō x

$$x\in \left(\frac{7}{3},\frac{31}{10}\right)$$

Ngā Upane Otinga

Kāore e taea a te tauraro 3x-7 te numa kore nā te mea kāore te rituatanga mā te kore e tautuhi. E rua ngā kēhi.

$$3x-7>0 3x-7<0$$

Whakaarohia te kēhi i ngā wā kei te tōrunga a 3x-7. Neke atu a -7 ki te taha matau.

$$3x>7$$

Whakawehea ngā taha e rua ki te 3. I te mea he tōrunga te 3, kāore e huri te ahunga koreōrite.

$$x>\frac{7}{3}$$

Kāore te tōrite tuatahi e whakarerekē te aronga ina e whakarea ana mā 3x-7 mō 3x-7>0.

$$2x+3>4\left(3x-7\right)$$

Whakarea te katoa o te taha matau.

$$2x+3>12x-28$$

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

$$2x-12x>-3-28$$

Pahekotia ngā kīanga tau ōrite.

$$-10x>-31$$

Whakawehea ngā taha e rua ki te -10. I te mea he tōraro a -10, ka huri te ahunga koreōrite.

$$x<\frac{31}{10}$$

Whakaarohia te herenga x>\frac{7}{3} e tautuhi ana ki runga.

$$x\in \left(\frac{7}{3},\frac{31}{10}\right)$$

Tēnā, me whakaarohia te tauira ina e tōraro a 3x-7. Neke atu a -7 ki te taha matau.

$$3x<7$$

Whakawehea ngā taha e rua ki te 3. I te mea he tōrunga te 3, kāore e huri te ahunga koreōrite.

$$x<\frac{7}{3}$$

E whakarerekē ana te aronga o te tōrite tuatahi hei ngā wā e whakarea ana a 3x-7 mō 3x-7<0.

$$2x+3<4\left(3x-7\right)$$

Whakarea te katoa o te taha matau.

$$2x+3<12x-28$$

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

$$2x-12x<-3-28$$

Pahekotia ngā kīanga tau ōrite.

$$-10x<-31$$

Whakawehea ngā taha e rua ki te -10. I te mea he tōraro a -10, ka huri te ahunga koreōrite.

$$x>\frac{31}{10}$$

Whakaarohia te herenga x<\frac{7}{3} e tautuhi ana ki runga.

$$x\in \emptyset$$

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

$$x\in \left(\frac{7}{3},\frac{31}{10}\right)$$