Whakaoti i te 6(4-3x)-5(x-3)geq3(7-x)-4(x-5)+46

$$6(4-3x)-5(x-3) \geq 3(7-x)-4(x-5)+46$$

Whakaoti mō x

$$x\leq -3$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te 4-3x.

$$24-18x-5\left(x-3\right)\geq 3\left(7-x\right)-4\left(x-5\right)+46$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te x-3.

$$24-18x-5x+15\geq 3\left(7-x\right)-4\left(x-5\right)+46$$

Pahekotia te -18x me -5x, ka -23x.

$$24-23x+15\geq 3\left(7-x\right)-4\left(x-5\right)+46$$

Tāpirihia te 24 ki te 15, ka 39.

$$39-23x\geq 3\left(7-x\right)-4\left(x-5\right)+46$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 7-x.

$$39-23x\geq 21-3x-4\left(x-5\right)+46$$

Whakamahia te āhuatanga tohatoha hei whakarea te -4 ki te x-5.

$$39-23x\geq 21-3x-4x+20+46$$

Pahekotia te -3x me -4x, ka -7x.

$$39-23x\geq 21-7x+20+46$$

Tāpirihia te 21 ki te 20, ka 41.

$$39-23x\geq 41-7x+46$$

Tāpirihia te 41 ki te 46, ka 87.

$$39-23x\geq 87-7x$$

Me tāpiri te 7x ki ngā taha e rua.

$$39-23x+7x\geq 87$$

Pahekotia te -23x me 7x, ka -16x.

$$39-16x\geq 87$$

Tangohia te 39 mai i ngā taha e rua.

$$-16x\geq 87-39$$

Tangohia te 39 i te 87, ka 48.

$$-16x\geq 48$$

Whakawehea ngā taha e rua ki te -16. I te mea he tōraro a -16, ka huri te ahunga koreōrite.

$$x\leq \frac{48}{-16}$$

Whakawehea te 48 ki te -16, kia riro ko -3.

$$x\leq -3$$