Whakaoti i te x/6-3(x+2)/5-4(2x+1)/15=3(3x+2)/10-frac{4}{3}

$$\frac { x } { 6 } - \frac { 3 ( x + 2 ) } { 5 } - \frac { 4 ( 2 x + 1 ) } { 15 } = \frac { 3 ( 3 x + 2 ) } { 10 } - \frac { 4 } { 3 }$$

Whakaoti mō x

$$x=-\frac{11}{28}\approx -0.392857143$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 30, arā, te tauraro pātahi he tino iti rawa te kitea o 6,5,15,10,3.

$$5x-6\times 3\left(x+2\right)-2\times 4\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Whakareatia te -6 ki te 3, ka -18.

$$5x-18\left(x+2\right)-2\times 4\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Whakamahia te āhuatanga tohatoha hei whakarea te -18 ki te x+2.

$$5x-18x-36-2\times 4\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Pahekotia te 5x me -18x, ka -13x.

$$-13x-36-2\times 4\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Whakareatia te -2 ki te 4, ka -8.

$$-13x-36-8\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Whakamahia te āhuatanga tohatoha hei whakarea te -8 ki te 2x+1.

$$-13x-36-16x-8=3\times 3\left(3x+2\right)-40$$

Pahekotia te -13x me -16x, ka -29x.

$$-29x-36-8=3\times 3\left(3x+2\right)-40$$

Tangohia te 8 i te -36, ka -44.

$$-29x-44=3\times 3\left(3x+2\right)-40$$

Whakareatia te 3 ki te 3, ka 9.

$$-29x-44=9\left(3x+2\right)-40$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te 3x+2.

$$-29x-44=27x+18-40$$

Tangohia te 40 i te 18, ka -22.

$$-29x-44=27x-22$$

Tangohia te 27x mai i ngā taha e rua.

$$-29x-44-27x=-22$$

Pahekotia te -29x me -27x, ka -56x.

$$-56x-44=-22$$

Me tāpiri te 44 ki ngā taha e rua.

$$-56x=-22+44$$

Tāpirihia te -22 ki te 44, ka 22.

$$-56x=22$$

Whakawehea ngā taha e rua ki te -56.

$$x=\frac{22}{-56}$$

Whakahekea te hautanga \frac{22}{-56} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{11}{28}$$