Whakaoti i te 2/3(x+1)-5/6(x-7)leq2

$$\frac { 2 } { 3 } ( x + 1 ) - \frac { 5 } { 6 } ( x - 7 ) \leq 2$$

Whakaoti mō x

$$x\geq 27$$

Ngā Upane Otinga

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

$$\frac{2}{3}x+\frac{2}{3}-\frac{5}{6}\left(x-7\right)\leq 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{5}{6} ki te x-7.

$$\frac{2}{3}x+\frac{2}{3}-\frac{5}{6}x-\frac{5}{6}\left(-7\right)\leq 2$$

Tuhia te -\frac{5}{6}\left(-7\right) hei hautanga kotahi.

$$\frac{2}{3}x+\frac{2}{3}-\frac{5}{6}x+\frac{-5\left(-7\right)}{6}\leq 2$$

Whakareatia te -5 ki te -7, ka 35.

$$\frac{2}{3}x+\frac{2}{3}-\frac{5}{6}x+\frac{35}{6}\leq 2$$

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

$$-\frac{1}{6}x+\frac{2}{3}+\frac{35}{6}\leq 2$$

Ko te maha noa iti rawa atu o 3 me 6 ko 6. Me tahuri \frac{2}{3} me \frac{35}{6} ki te hautau me te tautūnga 6.

$$-\frac{1}{6}x+\frac{4}{6}+\frac{35}{6}\leq 2$$

Tā te mea he rite te tauraro o \frac{4}{6} me \frac{35}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$-\frac{1}{6}x+\frac{4+35}{6}\leq 2$$

Tāpirihia te 4 ki te 35, ka 39.

$$-\frac{1}{6}x+\frac{39}{6}\leq 2$$

Whakahekea te hautanga \frac{39}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$-\frac{1}{6}x+\frac{13}{2}\leq 2$$

Tangohia te \frac{13}{2} mai i ngā taha e rua.

$$-\frac{1}{6}x\leq 2-\frac{13}{2}$$

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

$$-\frac{1}{6}x\leq \frac{4}{2}-\frac{13}{2}$$

Tā te mea he rite te tauraro o \frac{4}{2} me \frac{13}{2}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{1}{6}x\leq \frac{4-13}{2}$$

Tangohia te 13 i te 4, ka -9.

$$-\frac{1}{6}x\leq -\frac{9}{2}$$

Me whakarea ngā taha e rua ki te -6, te tau utu o -\frac{1}{6}. I te mea he tōraro a -\frac{1}{6}, ka huri te ahunga koreōrite.

$$x\geq -\frac{9}{2}\left(-6\right)$$

Tuhia te -\frac{9}{2}\left(-6\right) hei hautanga kotahi.

$$x\geq \frac{-9\left(-6\right)}{2}$$

Whakareatia te -9 ki te -6, ka 54.

$$x\geq \frac{54}{2}$$

Whakawehea te 54 ki te 2, kia riro ko 27.

$$x\geq 27$$