Whakaoti i te x-pi/x-4leqtan(1)

$$\frac{ x- \pi }{ x-4 } \leq \tan ( 1 )$$

Whakaoti mō x

$$x\in [\frac{200000000000000000\pi -13964051942574068}{196508987014356483},4)$$

Ngā Upane Otinga

Evaluate trigonometric functions in the problem

$$\frac{x - \pi}{x - 4} \leq 0.017455064928217585$$

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.

$$x-\pi \leq 0.017455064928217585\left(x-4\right)$$

Whakarea te katoa o te taha matau.

$$x-\pi \leq 0.017455064928217585x-0.06982025971287034$$

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

$$x-0.017455064928217585x\leq \pi -0.06982025971287034$$

Pahekotia ngā kīanga tau ōrite.

$$0.982544935071782415x\leq \pi -0.06982025971287034$$

Whakawehea ngā taha e rua ki te 0.982544935071782415. I te mea he tōrunga te 0.982544935071782415, kāore e huri te ahunga koreōrite.

$$x\leq \frac{200000000000000000\pi -13964051942574068}{196508987014356483}$$

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

$$x\in \emptyset$$

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.

$$x-\pi \geq 0.017455064928217585\left(x-4\right)$$

Whakarea te katoa o te taha matau.

$$x-\pi \geq 0.017455064928217585x-0.06982025971287034$$

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

$$x-0.017455064928217585x\geq \pi -0.06982025971287034$$

Pahekotia ngā kīanga tau ōrite.

$$0.982544935071782415x\geq \pi -0.06982025971287034$$

Whakawehea ngā taha e rua ki te 0.982544935071782415. I te mea he tōrunga te 0.982544935071782415, kāore e huri te ahunga koreōrite.

$$x\geq \frac{200000000000000000\pi -13964051942574068}{196508987014356483}$$

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

$$x\in [\frac{200000000000000000\pi -13964051942574068}{196508987014356483},4)$$

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

$$x\in [\frac{200000000000000000\pi -13964051942574068}{196508987014356483},4)$$