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

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

Whakaoti mō x

$$x<23$$

Ngā Upane Otinga

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

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

Whakaarohia te \left(x-5\right)\left(x+5\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 5.

$$x^{2}-x-2>x^{2}-25$$

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

$$x^{2}-x-2-x^{2}>-25$$

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

$$-x-2>-25$$

Me tāpiri te 2 ki ngā taha e rua.

$$-x>-25+2$$

Tāpirihia te -25 ki te 2, ka -23.

$$-x>-23$$

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

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

Ka taea te hautanga \frac{-23}{-1} te whakamāmā ki te 23 mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x<23$$