Whakaoti i te {l}{5[3(2-3x)-2(5-x)]-6(5(x-2)}{-2(4x-3)]<3x+19}

$$\left. \begin{array} { l } { 5 [ 3 ( 2 - 3 x ) - 2 ( 5 - x ) ] - 6 ( 5 ( x - 2 ) } \\ { - 2 ( 4 x - 3 ) ] < 3 x + 19 } \end{array} \right.$$

Whakaoti mō x

$$x>-\frac{3}{4}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 2-3x.

$$5\left(6-9x-2\left(5-x\right)\right)-6\left(5\left(x-2\right)-2\left(4x-3\right)\right)<3x+19$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 5-x.

$$5\left(6-9x-10+2x\right)-6\left(5\left(x-2\right)-2\left(4x-3\right)\right)<3x+19$$

Tangohia te 10 i te 6, ka -4.

$$5\left(-4-9x+2x\right)-6\left(5\left(x-2\right)-2\left(4x-3\right)\right)<3x+19$$

Pahekotia te -9x me 2x, ka -7x.

$$5\left(-4-7x\right)-6\left(5\left(x-2\right)-2\left(4x-3\right)\right)<3x+19$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te -4-7x.

$$-20-35x-6\left(5\left(x-2\right)-2\left(4x-3\right)\right)<3x+19$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x-2.

$$-20-35x-6\left(5x-10-2\left(4x-3\right)\right)<3x+19$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 4x-3.

$$-20-35x-6\left(5x-10-8x+6\right)<3x+19$$

Pahekotia te 5x me -8x, ka -3x.

$$-20-35x-6\left(-3x-10+6\right)<3x+19$$

Tāpirihia te -10 ki te 6, ka -4.

$$-20-35x-6\left(-3x-4\right)<3x+19$$

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

$$-20-35x+18x+24<3x+19$$

Pahekotia te -35x me 18x, ka -17x.

$$-20-17x+24<3x+19$$

Tāpirihia te -20 ki te 24, ka 4.

$$4-17x<3x+19$$

Tangohia te 3x mai i ngā taha e rua.

$$4-17x-3x<19$$

Pahekotia te -17x me -3x, ka -20x.

$$4-20x<19$$

Tangohia te 4 mai i ngā taha e rua.

$$-20x<19-4$$

Tangohia te 4 i te 19, ka 15.

$$-20x<15$$

Whakawehea ngā taha e rua ki te -20. I te mea he tōraro a -20, ka huri te ahunga koreōrite.

$$x>\frac{15}{-20}$$

Whakahekea te hautanga \frac{15}{-20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x>-\frac{3}{4}$$