Whakaoti i te 2x+1/x-2geq3

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

Whakaoti mō x

$$x\in (2,7]$$

Ngā Upane Otinga

Kāore e taea a te tauraro x-2 te numa kore nā te mea kāore te rituatanga mā te kore e tautuhi. E rua ngā kēhi.

$$x-2>0 x-2<0$$

Whakaarohia te kēhi i ngā wā kei te tōrunga a x-2. Neke atu a -2 ki te taha matau.

$$x>2$$

Kāore te tōrite tuatahi e whakarerekē te aronga ina e whakarea ana mā x-2 mō x-2>0.

$$2x+1\geq 3\left(x-2\right)$$

Whakarea te katoa o te taha matau.

$$2x+1\geq 3x-6$$

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

$$2x-3x\geq -1-6$$

Pahekotia ngā kīanga tau ōrite.

$$-x\geq -7$$

Whakawehea ngā taha e rua ki te -1. I te mea he tōraro a -1, ka huri te ahunga koreōrite.

$$x\leq 7$$

Whakaarohia te herenga x>2 e tautuhi ana ki runga.

$$x\in (2,7]$$

Tēnā, me whakaarohia te tauira ina e tōraro a x-2. Neke atu a -2 ki te taha matau.

$$x<2$$

E whakarerekē ana te aronga o te tōrite tuatahi hei ngā wā e whakarea ana a x-2 mō x-2<0.

$$2x+1\leq 3\left(x-2\right)$$

Whakarea te katoa o te taha matau.

$$2x+1\leq 3x-6$$

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

$$2x-3x\leq -1-6$$

Pahekotia ngā kīanga tau ōrite.

$$-x\leq -7$$

Whakawehea ngā taha e rua ki te -1. I te mea he tōraro a -1, ka huri te ahunga koreōrite.

$$x\geq 7$$

Whakaarohia te herenga x<2 e tautuhi ana ki runga.

$$x\in \emptyset$$

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

$$x\in (2,7]$$