Whakaoti i te 5/9x-5/3=3/4x-1/2

$$\frac{ 5 }{ 9 } x- \frac{ 5 }{ 3 } = \frac{ 3 }{ 4 } x- \frac{ 1 }{ 2 }$$

Whakaoti mō x

$$x=-6$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \frac{3}{4}x mai i ngā taha e rua.

$$\frac{5}{9}x-\frac{5}{3}-\frac{3}{4}x=-\frac{1}{2}$$

Pahekotia te \frac{5}{9}x me -\frac{3}{4}x, ka -\frac{7}{36}x.

$$-\frac{7}{36}x-\frac{5}{3}=-\frac{1}{2}$$

Me tāpiri te \frac{5}{3} ki ngā taha e rua.

$$-\frac{7}{36}x=-\frac{1}{2}+\frac{5}{3}$$

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri -\frac{1}{2} me \frac{5}{3} ki te hautau me te tautūnga 6.

$$-\frac{7}{36}x=-\frac{3}{6}+\frac{10}{6}$$

Tā te mea he rite te tauraro o -\frac{3}{6} me \frac{10}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$-\frac{7}{36}x=\frac{-3+10}{6}$$

Tāpirihia te -3 ki te 10, ka 7.

$$-\frac{7}{36}x=\frac{7}{6}$$

Me whakarea ngā taha e rua ki te -\frac{36}{7}, te tau utu o -\frac{7}{36}.

$$x=\frac{7}{6}\left(-\frac{36}{7}\right)$$

Me whakarea te \frac{7}{6} ki te -\frac{36}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{7\left(-36\right)}{6\times 7}$$

Me whakakore tahi te 7 i te taurunga me te tauraro.

$$x=\frac{-36}{6}$$

Whakawehea te -36 ki te 6, kia riro ko -6.

$$x=-6$$