Whakaoti i te (x-2)-1/2(x+1)=5/6(x+2)

$$( x - 2 ) - \frac { 1 } { 2 } ( x + 1 ) = \frac { 5 } { 6 } ( x + 2 )$$

Whakaoti mō x

$$x = -\frac{25}{2} = -12\frac{1}{2} = -12.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

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

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

Tā te mea he rite te tauraro o -\frac{4}{2} me \frac{1}{2}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te -4, ka -5.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{5}{6} ki te x+2.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{5}{6}\times 2$$

Tuhia te \frac{5}{6}\times 2 hei hautanga kotahi.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{5\times 2}{6}$$

Whakareatia te 5 ki te 2, ka 10.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{10}{6}$$

Whakahekea te hautanga \frac{10}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{5}{3}$$

Tangohia te \frac{5}{6}x mai i ngā taha e rua.

$$\frac{1}{2}x-\frac{5}{2}-\frac{5}{6}x=\frac{5}{3}$$

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

$$-\frac{1}{3}x-\frac{5}{2}=\frac{5}{3}$$

Me tāpiri te \frac{5}{2} ki ngā taha e rua.

$$-\frac{1}{3}x=\frac{5}{3}+\frac{5}{2}$$

Ko te maha noa iti rawa atu o 3 me 2 ko 6. Me tahuri \frac{5}{3} me \frac{5}{2} ki te hautau me te tautūnga 6.

$$-\frac{1}{3}x=\frac{10}{6}+\frac{15}{6}$$

Tā te mea he rite te tauraro o \frac{10}{6} me \frac{15}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$-\frac{1}{3}x=\frac{10+15}{6}$$

Tāpirihia te 10 ki te 15, ka 25.

$$-\frac{1}{3}x=\frac{25}{6}$$

Me whakarea ngā taha e rua ki te -3, te tau utu o -\frac{1}{3}.

$$x=\frac{25}{6}\left(-3\right)$$

Tuhia te \frac{25}{6}\left(-3\right) hei hautanga kotahi.

$$x=\frac{25\left(-3\right)}{6}$$

Whakareatia te 25 ki te -3, ka -75.

$$x=\frac{-75}{6}$$

Whakahekea te hautanga \frac{-75}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=-\frac{25}{2}$$