Whakaoti i te 5/6left(3-xright)-1/2left(x-4right)geq1/2(2x-3)-x

$$\frac{ 5 }{ 6 } \left( 3-x \right) - \frac{ 1 }{ 2 } \left( x-4 \right) \geq \frac{ 1 }{ 2 } (2x-3)-x$$

Whakaoti mō x

$$x\leq \frac{9}{2}$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{5}{6} ki te 3-x.

$$\frac{5}{6}\times 3+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}\left(2x-3\right)-x$$

Tuhia te \frac{5}{6}\times 3 hei hautanga kotahi.

$$\frac{5\times 3}{6}+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}\left(2x-3\right)-x$$

Whakareatia te 5 ki te 3, ka 15.

$$\frac{15}{6}+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}\left(2x-3\right)-x$$

Whakahekea te hautanga \frac{15}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{5}{2}+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}\left(2x-3\right)-x$$

Whakareatia te \frac{5}{6} ki te -1, ka -\frac{5}{6}.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}\left(2x-3\right)-x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{2} ki te x-4.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}x-\frac{1}{2}\left(-4\right)\geq \frac{1}{2}\left(2x-3\right)-x$$

Tuhia te -\frac{1}{2}\left(-4\right) hei hautanga kotahi.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}x+\frac{-\left(-4\right)}{2}\geq \frac{1}{2}\left(2x-3\right)-x$$

Whakareatia te -1 ki te -4, ka 4.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}x+\frac{4}{2}\geq \frac{1}{2}\left(2x-3\right)-x$$

Whakawehea te 4 ki te 2, kia riro ko 2.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}x+2\geq \frac{1}{2}\left(2x-3\right)-x$$

Pahekotia te -\frac{5}{6}x me -\frac{1}{2}x, ka -\frac{4}{3}x.

$$\frac{5}{2}-\frac{4}{3}x+2\geq \frac{1}{2}\left(2x-3\right)-x$$

Me tahuri te 2 ki te hautau \frac{4}{2}.

$$\frac{5}{2}-\frac{4}{3}x+\frac{4}{2}\geq \frac{1}{2}\left(2x-3\right)-x$$

Tā te mea he rite te tauraro o \frac{5}{2} me \frac{4}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5+4}{2}-\frac{4}{3}x\geq \frac{1}{2}\left(2x-3\right)-x$$

Tāpirihia te 5 ki te 4, ka 9.

$$\frac{9}{2}-\frac{4}{3}x\geq \frac{1}{2}\left(2x-3\right)-x$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 2x-3.

$$\frac{9}{2}-\frac{4}{3}x\geq \frac{1}{2}\times 2x+\frac{1}{2}\left(-3\right)-x$$

Me whakakore te 2 me te 2.

$$\frac{9}{2}-\frac{4}{3}x\geq x+\frac{1}{2}\left(-3\right)-x$$

Whakareatia te \frac{1}{2} ki te -3, ka \frac{-3}{2}.

$$\frac{9}{2}-\frac{4}{3}x\geq x+\frac{-3}{2}-x$$

Ka taea te hautanga \frac{-3}{2} te tuhi anō ko -\frac{3}{2} mā te tango i te tohu tōraro.

$$\frac{9}{2}-\frac{4}{3}x\geq x-\frac{3}{2}-x$$

Pahekotia te x me -x, ka 0.

$$\frac{9}{2}-\frac{4}{3}x\geq -\frac{3}{2}$$

Tangohia te \frac{9}{2} mai i ngā taha e rua.

$$-\frac{4}{3}x\geq -\frac{3}{2}-\frac{9}{2}$$

Tā te mea he rite te tauraro o -\frac{3}{2} me \frac{9}{2}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{4}{3}x\geq \frac{-3-9}{2}$$

Tangohia te 9 i te -3, ka -12.

$$-\frac{4}{3}x\geq \frac{-12}{2}$$

Whakawehea te -12 ki te 2, kia riro ko -6.

$$-\frac{4}{3}x\geq -6$$

Me whakarea ngā taha e rua ki te -\frac{3}{4}, te tau utu o -\frac{4}{3}. I te mea he tōraro a -\frac{4}{3}, ka huri te ahunga koreōrite.

$$x\leq -6\left(-\frac{3}{4}\right)$$

Tuhia te -6\left(-\frac{3}{4}\right) hei hautanga kotahi.

$$x\leq \frac{-6\left(-3\right)}{4}$$

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

$$x\leq \frac{18}{4}$$

Whakahekea te hautanga \frac{18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x\leq \frac{9}{2}$$