Whakaoti i te 1/2(x+1)+1/4(x+3)=3-1/3(x+2)

$$\frac { 1 } { 2 } ( x + 1 ) + \frac { 1 } { 4 } ( x + 3 ) = 3 - \frac { 1 } { 3 } ( x + 2 )$$

Whakaoti mō x

$$x=1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te x+3.

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

Whakareatia te \frac{1}{4} ki te 3, ka \frac{3}{4}.

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

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

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

Ko te maha noa iti rawa atu o 2 me 4 ko 4. Me tahuri \frac{1}{2} me \frac{3}{4} ki te hautau me te tautūnga 4.

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

Tā te mea he rite te tauraro o \frac{2}{4} me \frac{3}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te 2 ki te 3, ka 5.

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

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

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

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

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

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

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

Me tahuri te 3 ki te hautau \frac{9}{3}.

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

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

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

Tangohia te 2 i te 9, ka 7.

$$\frac{3}{4}x+\frac{5}{4}=\frac{7}{3}-\frac{1}{3}x$$

Me tāpiri te \frac{1}{3}x ki ngā taha e rua.

$$\frac{3}{4}x+\frac{5}{4}+\frac{1}{3}x=\frac{7}{3}$$

Pahekotia te \frac{3}{4}x me \frac{1}{3}x, ka \frac{13}{12}x.

$$\frac{13}{12}x+\frac{5}{4}=\frac{7}{3}$$

Tangohia te \frac{5}{4} mai i ngā taha e rua.

$$\frac{13}{12}x=\frac{7}{3}-\frac{5}{4}$$

Ko te maha noa iti rawa atu o 3 me 4 ko 12. Me tahuri \frac{7}{3} me \frac{5}{4} ki te hautau me te tautūnga 12.

$$\frac{13}{12}x=\frac{28}{12}-\frac{15}{12}$$

Tā te mea he rite te tauraro o \frac{28}{12} me \frac{15}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{13}{12}x=\frac{28-15}{12}$$

Tangohia te 15 i te 28, ka 13.

$$\frac{13}{12}x=\frac{13}{12}$$

Me whakarea ngā taha e rua ki te \frac{12}{13}, te tau utu o \frac{13}{12}.

$$x=\frac{13}{12}\times \frac{12}{13}$$

Me whakakore atu te \frac{13}{12} me tōna tau utu \frac{12}{13}.

$$x=1$$