Whakaoti i te 3/2(x+5)-1/3(x+2)=9/2

$$\frac{ 3 }{ 2 } (x+5)- \frac{ 1 }{ 3 } (x+2)= \frac{ 9 }{ 2 }$$

Whakaoti mō x

$$x=-2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{2} ki te x+5.

$$\frac{3}{2}x+\frac{3}{2}\times 5-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

Tuhia te \frac{3}{2}\times 5 hei hautanga kotahi.

$$\frac{3}{2}x+\frac{3\times 5}{2}-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

Whakareatia te 3 ki te 5, ka 15.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

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

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x-\frac{1}{3}\times 2=\frac{9}{2}$$

Tuhia te -\frac{1}{3}\times 2 hei hautanga kotahi.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x+\frac{-2}{3}=\frac{9}{2}$$

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

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x-\frac{2}{3}=\frac{9}{2}$$

Pahekotia te \frac{3}{2}x me -\frac{1}{3}x, ka \frac{7}{6}x.

$$\frac{7}{6}x+\frac{15}{2}-\frac{2}{3}=\frac{9}{2}$$

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri \frac{15}{2} me \frac{2}{3} ki te hautau me te tautūnga 6.

$$\frac{7}{6}x+\frac{45}{6}-\frac{4}{6}=\frac{9}{2}$$

Tā te mea he rite te tauraro o \frac{45}{6} me \frac{4}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{7}{6}x+\frac{45-4}{6}=\frac{9}{2}$$

Tangohia te 4 i te 45, ka 41.

$$\frac{7}{6}x+\frac{41}{6}=\frac{9}{2}$$

Tangohia te \frac{41}{6} mai i ngā taha e rua.

$$\frac{7}{6}x=\frac{9}{2}-\frac{41}{6}$$

Ko te maha noa iti rawa atu o 2 me 6 ko 6. Me tahuri \frac{9}{2} me \frac{41}{6} ki te hautau me te tautūnga 6.

$$\frac{7}{6}x=\frac{27}{6}-\frac{41}{6}$$

Tā te mea he rite te tauraro o \frac{27}{6} me \frac{41}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{7}{6}x=\frac{27-41}{6}$$

Tangohia te 41 i te 27, ka -14.

$$\frac{7}{6}x=\frac{-14}{6}$$

Whakahekea te hautanga \frac{-14}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{7}{6}x=-\frac{7}{3}$$

Me whakarea ngā taha e rua ki te \frac{6}{7}, te tau utu o \frac{7}{6}.

$$x=-\frac{7}{3}\times \frac{6}{7}$$

Me whakarea te -\frac{7}{3} ki te \frac{6}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-7\times 6}{3\times 7}$$

Mahia ngā whakarea i roto i te hautanga \frac{-7\times 6}{3\times 7}.

$$x=\frac{-42}{21}$$

Whakawehea te -42 ki te 21, kia riro ko -2.

$$x=-2$$