Whakaoti i te 1/5(3-3/2x)-3(2-5/4x)=36

$$\frac { 1 } { 5 } ( 3 - \frac { 3 } { 2 } x ) - 3 ( 2 - \frac { 5 } { 4 } x ) = 36$$

Whakaoti mō x

$$x=12$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{5} ki te 3-\frac{3}{2}x.

$$\frac{1}{5}\times 3+\frac{1}{5}\left(-\frac{3}{2}\right)x-3\left(2-\frac{5}{4}x\right)=36$$

Whakareatia te \frac{1}{5} ki te 3, ka \frac{3}{5}.

$$\frac{3}{5}+\frac{1}{5}\left(-\frac{3}{2}\right)x-3\left(2-\frac{5}{4}x\right)=36$$

Me whakarea te \frac{1}{5} ki te -\frac{3}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{3}{5}+\frac{1\left(-3\right)}{5\times 2}x-3\left(2-\frac{5}{4}x\right)=36$$

Mahia ngā whakarea i roto i te hautanga \frac{1\left(-3\right)}{5\times 2}.

$$\frac{3}{5}+\frac{-3}{10}x-3\left(2-\frac{5}{4}x\right)=36$$

Ka taea te hautanga \frac{-3}{10} te tuhi anō ko -\frac{3}{10} mā te tango i te tohu tōraro.

$$\frac{3}{5}-\frac{3}{10}x-3\left(2-\frac{5}{4}x\right)=36$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te 2-\frac{5}{4}x.

$$\frac{3}{5}-\frac{3}{10}x-6-3\left(-\frac{5}{4}\right)x=36$$

Tuhia te -3\left(-\frac{5}{4}\right) hei hautanga kotahi.

$$\frac{3}{5}-\frac{3}{10}x-6+\frac{-3\left(-5\right)}{4}x=36$$

Whakareatia te -3 ki te -5, ka 15.

$$\frac{3}{5}-\frac{3}{10}x-6+\frac{15}{4}x=36$$

Me tahuri te 6 ki te hautau \frac{30}{5}.

$$\frac{3}{5}-\frac{3}{10}x-\frac{30}{5}+\frac{15}{4}x=36$$

Tā te mea he rite te tauraro o \frac{3}{5} me \frac{30}{5}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3-30}{5}-\frac{3}{10}x+\frac{15}{4}x=36$$

Tangohia te 30 i te 3, ka -27.

$$-\frac{27}{5}-\frac{3}{10}x+\frac{15}{4}x=36$$

Pahekotia te -\frac{3}{10}x me \frac{15}{4}x, ka \frac{69}{20}x.

$$-\frac{27}{5}+\frac{69}{20}x=36$$

Me tāpiri te \frac{27}{5} ki ngā taha e rua.

$$\frac{69}{20}x=36+\frac{27}{5}$$

Me tahuri te 36 ki te hautau \frac{180}{5}.

$$\frac{69}{20}x=\frac{180}{5}+\frac{27}{5}$$

Tā te mea he rite te tauraro o \frac{180}{5} me \frac{27}{5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{69}{20}x=\frac{180+27}{5}$$

Tāpirihia te 180 ki te 27, ka 207.

$$\frac{69}{20}x=\frac{207}{5}$$

Me whakarea ngā taha e rua ki te \frac{20}{69}, te tau utu o \frac{69}{20}.

$$x=\frac{207}{5}\times \frac{20}{69}$$

Me whakarea te \frac{207}{5} ki te \frac{20}{69} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{207\times 20}{5\times 69}$$

Mahia ngā whakarea i roto i te hautanga \frac{207\times 20}{5\times 69}.

$$x=\frac{4140}{345}$$

Whakawehea te 4140 ki te 345, kia riro ko 12.

$$x=12$$