Whakaoti i te x-1/2x-1leq2/3

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

Whakaoti mō x

$$x\in (-\infty,-1]\cup (\frac{1}{2},\infty)$$

Ngā Upane Otinga

Kāore e taea a te tauraro 2x-1 te numa kore nā te mea kāore te rituatanga mā te kore e tautuhi. E rua ngā kēhi.

$$2x-1>0 2x-1<0$$

Whakaarohia te kēhi i ngā wā kei te tōrunga a 2x-1. Neke atu a -1 ki te taha matau.

$$2x>1$$

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

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

Kāore te tōrite tuatahi e whakarerekē te aronga ina e whakarea ana mā 2x-1 mō 2x-1>0.

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

Whakarea te katoa o te taha matau.

$$x-1\leq \frac{4}{3}x-\frac{2}{3}$$

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

$$x-\frac{4}{3}x\leq 1-\frac{2}{3}$$

Pahekotia ngā kīanga tau ōrite.

$$-\frac{1}{3}x\leq \frac{1}{3}$$

Whakawehea ngā taha e rua ki te -\frac{1}{3}. I te mea he tōraro a -\frac{1}{3}, ka huri te ahunga koreōrite.

$$x\geq -1$$

Whakaarohia te herenga x>\frac{1}{2} e tautuhi ana ki runga.

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

Tēnā, me whakaarohia te tauira ina e tōraro a 2x-1. Neke atu a -1 ki te taha matau.

$$2x<1$$

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

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

E whakarerekē ana te aronga o te tōrite tuatahi hei ngā wā e whakarea ana a 2x-1 mō 2x-1<0.

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

Whakarea te katoa o te taha matau.

$$x-1\geq \frac{4}{3}x-\frac{2}{3}$$

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

$$x-\frac{4}{3}x\geq 1-\frac{2}{3}$$

Pahekotia ngā kīanga tau ōrite.

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

Whakawehea ngā taha e rua ki te -\frac{1}{3}. I te mea he tōraro a -\frac{1}{3}, ka huri te ahunga koreōrite.

$$x\leq -1$$

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

$$x\in (-\infty,-1]\cup (\frac{1}{2},\infty)$$