Whakaoti i te 1/2[1+1/4(3z-1)]=2z/3-1/2

$$\frac { 1 } { 2 } [ 1 + \frac { 1 } { 4 } ( 3 z - 1 ) ] = \frac { 2 z } { 3 } - \frac { 1 } { 2 }$$

Whakaoti mō z

$$z=3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 2,4,3.

$$6\left(1+\frac{1}{4}\left(3z-1\right)\right)=4\times 2z-6$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te 3z-1.

$$6\left(1+\frac{1}{4}\times 3z+\frac{1}{4}\left(-1\right)\right)=4\times 2z-6$$

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

$$6\left(1+\frac{3}{4}z+\frac{1}{4}\left(-1\right)\right)=4\times 2z-6$$

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

$$6\left(1+\frac{3}{4}z-\frac{1}{4}\right)=4\times 2z-6$$

Me tahuri te 1 ki te hautau \frac{4}{4}.

$$6\left(\frac{4}{4}+\frac{3}{4}z-\frac{1}{4}\right)=4\times 2z-6$$

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

$$6\left(\frac{4-1}{4}+\frac{3}{4}z\right)=4\times 2z-6$$

Tangohia te 1 i te 4, ka 3.

$$6\left(\frac{3}{4}+\frac{3}{4}z\right)=4\times 2z-6$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te \frac{3}{4}+\frac{3}{4}z.

$$6\times \frac{3}{4}+6\times \frac{3}{4}z=4\times 2z-6$$

Tuhia te 6\times \frac{3}{4} hei hautanga kotahi.

$$\frac{6\times 3}{4}+6\times \frac{3}{4}z=4\times 2z-6$$

Whakareatia te 6 ki te 3, ka 18.

$$\frac{18}{4}+6\times \frac{3}{4}z=4\times 2z-6$$

Whakahekea te hautanga \frac{18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{9}{2}+6\times \frac{3}{4}z=4\times 2z-6$$

Tuhia te 6\times \frac{3}{4} hei hautanga kotahi.

$$\frac{9}{2}+\frac{6\times 3}{4}z=4\times 2z-6$$

Whakareatia te 6 ki te 3, ka 18.

$$\frac{9}{2}+\frac{18}{4}z=4\times 2z-6$$

Whakahekea te hautanga \frac{18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{9}{2}+\frac{9}{2}z=4\times 2z-6$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{9}{2}+\frac{9}{2}z=8z-6$$

Tangohia te 8z mai i ngā taha e rua.

$$\frac{9}{2}+\frac{9}{2}z-8z=-6$$

Pahekotia te \frac{9}{2}z me -8z, ka -\frac{7}{2}z.

$$\frac{9}{2}-\frac{7}{2}z=-6$$

Tangohia te \frac{9}{2} mai i ngā taha e rua.

$$-\frac{7}{2}z=-6-\frac{9}{2}$$

Me tahuri te -6 ki te hautau -\frac{12}{2}.

$$-\frac{7}{2}z=-\frac{12}{2}-\frac{9}{2}$$

Tā te mea he rite te tauraro o -\frac{12}{2} me \frac{9}{2}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{7}{2}z=\frac{-12-9}{2}$$

Tangohia te 9 i te -12, ka -21.

$$-\frac{7}{2}z=-\frac{21}{2}$$

Me whakarea ngā taha e rua ki te -\frac{2}{7}, te tau utu o -\frac{7}{2}.

$$z=-\frac{21}{2}\left(-\frac{2}{7}\right)$$

Me whakarea te -\frac{21}{2} ki te -\frac{2}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$z=\frac{-21\left(-2\right)}{2\times 7}$$

Mahia ngā whakarea i roto i te hautanga \frac{-21\left(-2\right)}{2\times 7}.

$$z=\frac{42}{14}$$

Whakawehea te 42 ki te 14, kia riro ko 3.

$$z=3$$