Whakaoti i te -3x+2/x-4geq-5

$$\frac{ -3x+2 }{ x-4 } \geq -5$$

Whakaoti mō x

$$x\in (-\infty,4)\cup [9,\infty)$$

Ngā Upane Otinga

Kāore e taea a te tauraro x-4 te numa kore nā te mea kāore te rituatanga mā te kore e tautuhi. E rua ngā kēhi.

$$x-4>0 x-4<0$$

Whakaarohia te kēhi i ngā wā kei te tōrunga a x-4. Neke atu a -4 ki te taha matau.

$$x>4$$

Kāore te tōrite tuatahi e whakarerekē te aronga ina e whakarea ana mā x-4 mō x-4>0.

$$-3x+2\geq -5\left(x-4\right)$$

Whakarea te katoa o te taha matau.

$$-3x+2\geq -5x+20$$

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

$$-3x+5x\geq -2+20$$

Pahekotia ngā kīanga tau ōrite.

$$2x\geq 18$$

Whakawehea ngā taha e rua ki te 2. I te mea he tōrunga te 2, kāore e huri te ahunga koreōrite.

$$x\geq 9$$

Tēnā, me whakaarohia te tauira ina e tōraro a x-4. Neke atu a -4 ki te taha matau.

$$x<4$$

E whakarerekē ana te aronga o te tōrite tuatahi hei ngā wā e whakarea ana a x-4 mō x-4<0.

$$-3x+2\leq -5\left(x-4\right)$$

Whakarea te katoa o te taha matau.

$$-3x+2\leq -5x+20$$

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

$$-3x+5x\leq -2+20$$

Pahekotia ngā kīanga tau ōrite.

$$2x\leq 18$$

Whakawehea ngā taha e rua ki te 2. I te mea he tōrunga te 2, kāore e huri te ahunga koreōrite.

$$x\leq 9$$

Whakaarohia te herenga x<4 e tautuhi ana ki runga.

$$x<4$$

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

$$x\in (-\infty,4)\cup [9,\infty)$$