Whakaoti i te 4/5x+1/10<3/2x

$$\frac{ 4 }{ 5x } + \frac{ 1 }{ 10 } < \frac{ 3 }{ 2x }$$

Whakaoti mō x

$$x\in \left(0,7\right)$$

Ngā Upane Otinga

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 5x me 10 ko 10x. Whakareatia \frac{4}{5x} ki te \frac{2}{2}. Whakareatia \frac{1}{10} ki te \frac{x}{x}.

$$\frac{4\times 2}{10x}+\frac{x}{10x}<\frac{3}{2x}$$

Tā te mea he rite te tauraro o \frac{4\times 2}{10x} me \frac{x}{10x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4\times 2+x}{10x}<\frac{3}{2x}$$

Mahia ngā whakarea i roto o 4\times 2+x.

$$\frac{8+x}{10x}<\frac{3}{2x}$$

Tangohia te \frac{3}{2x} mai i ngā taha e rua.

$$\frac{8+x}{10x}-\frac{3}{2x}<0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 10x me 2x ko 10x. Whakareatia \frac{3}{2x} ki te \frac{5}{5}.

$$\frac{8+x}{10x}-\frac{3\times 5}{10x}<0$$

Tā te mea he rite te tauraro o \frac{8+x}{10x} me \frac{3\times 5}{10x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{8+x-3\times 5}{10x}<0$$

Mahia ngā whakarea i roto o 8+x-3\times 5.

$$\frac{8+x-15}{10x}<0$$

Whakakotahitia ngā kupu rite i 8+x-15.

$$\frac{-7+x}{10x}<0$$

Kia tōraro ai te otinga, hei tauaro hoki ngā tohu o x-7 me 10x. Whakaarohia te tauira ina he tōrunga te x-7 he tōraro te 10x.

$$x-7>0 10x<0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina he tōrunga te 10x he tōraro te x-7.

$$10x>0 x-7<0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left(0,7\right).

$$x\in \left(0,7\right)$$

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

$$x\in \left(0,7\right)$$