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

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

Whakaoti mō x

$$x = \frac{29}{4} = 7\frac{1}{4} = 7.25$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Whakareatia te 3 ki te \frac{1}{2}, ka \frac{3}{2}.

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

Hei kimi i te tauaro o 1+x, kimihia te tauaro o ia taurangi.

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

Tangohia te 1 i te -3, ka -4.

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

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

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

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

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

Whakareatia te \frac{1}{3} ki te 2, ka \frac{2}{3}.

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

Me whakarea te \frac{1}{3} ki te \frac{1}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{1\times 1}{3\times 2}.

$$\frac{1}{2}x-4+\frac{2}{3}x+\frac{1}{6}=\frac{1}{2}x+1$$

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

$$\frac{7}{6}x-4+\frac{1}{6}=\frac{1}{2}x+1$$

Me tahuri te -4 ki te hautau -\frac{24}{6}.

$$\frac{7}{6}x-\frac{24}{6}+\frac{1}{6}=\frac{1}{2}x+1$$

Tā te mea he rite te tauraro o -\frac{24}{6} me \frac{1}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7}{6}x+\frac{-24+1}{6}=\frac{1}{2}x+1$$

Tāpirihia te -24 ki te 1, ka -23.

$$\frac{7}{6}x-\frac{23}{6}=\frac{1}{2}x+1$$

Tangohia te \frac{1}{2}x mai i ngā taha e rua.

$$\frac{7}{6}x-\frac{23}{6}-\frac{1}{2}x=1$$

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

$$\frac{2}{3}x-\frac{23}{6}=1$$

Me tāpiri te \frac{23}{6} ki ngā taha e rua.

$$\frac{2}{3}x=1+\frac{23}{6}$$

Me tahuri te 1 ki te hautau \frac{6}{6}.

$$\frac{2}{3}x=\frac{6}{6}+\frac{23}{6}$$

Tā te mea he rite te tauraro o \frac{6}{6} me \frac{23}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2}{3}x=\frac{6+23}{6}$$

Tāpirihia te 6 ki te 23, ka 29.

$$\frac{2}{3}x=\frac{29}{6}$$

Me whakarea ngā taha e rua ki te \frac{3}{2}, te tau utu o \frac{2}{3}.

$$x=\frac{29}{6}\times \frac{3}{2}$$

Me whakarea te \frac{29}{6} ki te \frac{3}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{29\times 3}{6\times 2}$$

Mahia ngā whakarea i roto i te hautanga \frac{29\times 3}{6\times 2}.

$$x=\frac{87}{12}$$

Whakahekea te hautanga \frac{87}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=\frac{29}{4}$$