Whakaoti i te (4x+1)(2x-2)>8x(x+5)

$$( 4 x + 1 ) ( 2 x - 2 ) > 8 x ( x + 5 )$$

Whakaoti mō x

$$x<-\frac{1}{23}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+1 ki te 2x-2 ka whakakotahi i ngā kupu rite.

$$8x^{2}-6x-2>8x\left(x+5\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8x ki te x+5.

$$8x^{2}-6x-2>8x^{2}+40x$$

Tangohia te 8x^{2} mai i ngā taha e rua.

$$8x^{2}-6x-2-8x^{2}>40x$$

Pahekotia te 8x^{2} me -8x^{2}, ka 0.

$$-6x-2>40x$$

Tangohia te 40x mai i ngā taha e rua.

$$-6x-2-40x>0$$

Pahekotia te -6x me -40x, ka -46x.

$$-46x-2>0$$

Me tāpiri te 2 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-46x>2$$

Whakawehea ngā taha e rua ki te -46. I te mea he tōraro a -46, ka huri te ahunga koreōrite.

$$x<\frac{2}{-46}$$

Whakahekea te hautanga \frac{2}{-46} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x<-\frac{1}{23}$$