Whakaoti i te (1/2-x):x=[2/7*(1-1/5)]:[(1-3/5):(1+frac{2}{5})]

$$( \frac { 1 } { 2 } - x ) : x = [ \frac { 2 } { 7 } \cdot ( 1 - \frac { 1 } { 5 } ) ] : [ ( 1 - \frac { 3 } { 5 } ) : ( 1 + \frac { 2 } { 5 } ) ]$$

Whakaoti mō x

$$x=\frac{5}{18}\approx 0.277777778$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$\frac{1}{2}-x=\frac{7}{2}x\times \frac{2}{7}\left(1-\frac{1}{5}\right)$$

Me whakakore atu te \frac{7}{2} me tōna tau utu \frac{2}{7}.

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

Me tahuri te 1 ki te hautau \frac{5}{5}.

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

Tā te mea he rite te tauraro o \frac{5}{5} me \frac{1}{5}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 5, ka 4.

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

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

$$\frac{1}{2}-x-x\times \frac{4}{5}=0$$

Pahekotia te -x me -x\times \frac{4}{5}, ka -\frac{9}{5}x.

$$\frac{1}{2}-\frac{9}{5}x=0$$

Tangohia te \frac{1}{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Me whakarea ngā taha e rua ki te -\frac{5}{9}, te tau utu o -\frac{9}{5}.

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

Me whakarea te -\frac{1}{2} ki te -\frac{5}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{-\left(-5\right)}{2\times 9}.

$$x=\frac{5}{18}$$