Whakaoti i te 0.04x+0.09/0.05-0.3x+0.2/0.3=x-5/2

$$\frac { 0.04 x + 0.09 } { 0.05 } - \frac { 0.3 x + 0.2 } { 0.3 } = \frac { x - 5 } { 2 }$$

Whakaoti mō x

$$x = \frac{109}{21} = 5\frac{4}{21} \approx 5.19047619$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2\times \frac{0.04x+0.09}{0.05}-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Whakawehea ia wā o 0.04x+0.09 ki te 0.05, kia riro ko \frac{0.04x}{0.05}+\frac{0.09}{0.05}.

$$2\left(\frac{0.04x}{0.05}+\frac{0.09}{0.05}\right)-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Whakawehea te 0.04x ki te 0.05, kia riro ko 0.8x.

$$2\left(0.8x+\frac{0.09}{0.05}\right)-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Whakarohaina te \frac{0.09}{0.05} mā te whakarea i te taurunga me te tauraro ki te 100.

$$2\left(0.8x+\frac{9}{5}\right)-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 0.8x+\frac{9}{5}.

$$1.6x+2\times \frac{9}{5}-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Tuhia te 2\times \frac{9}{5} hei hautanga kotahi.

$$1.6x+\frac{2\times 9}{5}-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Whakareatia te 2 ki te 9, ka 18.

$$1.6x+\frac{18}{5}-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Whakawehea ia wā o 0.3x+0.2 ki te 0.3, kia riro ko \frac{0.3x}{0.3}+\frac{0.2}{0.3}.

$$1.6x+\frac{18}{5}-2\left(\frac{0.3x}{0.3}+\frac{0.2}{0.3}\right)=x-5$$

Me whakakore te 0.3 me te 0.3.

$$1.6x+\frac{18}{5}-2\left(x+\frac{0.2}{0.3}\right)=x-5$$

Whakarohaina te \frac{0.2}{0.3} mā te whakarea i te taurunga me te tauraro ki te 10.

$$1.6x+\frac{18}{5}-2\left(x+\frac{2}{3}\right)=x-5$$

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

$$1.6x+\frac{18}{5}-2x-2\times \frac{2}{3}=x-5$$

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

$$1.6x+\frac{18}{5}-2x+\frac{-2\times 2}{3}=x-5$$

Whakareatia te -2 ki te 2, ka -4.

$$1.6x+\frac{18}{5}-2x+\frac{-4}{3}=x-5$$

Ka taea te hautanga \frac{-4}{3} te tuhi anō ko -\frac{4}{3} mā te tango i te tohu tōraro.

$$1.6x+\frac{18}{5}-2x-\frac{4}{3}=x-5$$

Pahekotia te 1.6x me -2x, ka -0.4x.

$$-0.4x+\frac{18}{5}-\frac{4}{3}=x-5$$

Ko te maha noa iti rawa atu o 5 me 3 ko 15. Me tahuri \frac{18}{5} me \frac{4}{3} ki te hautau me te tautūnga 15.

$$-0.4x+\frac{54}{15}-\frac{20}{15}=x-5$$

Tā te mea he rite te tauraro o \frac{54}{15} me \frac{20}{15}, me tango rāua mā te tango i ō raua taurunga.

$$-0.4x+\frac{54-20}{15}=x-5$$

Tangohia te 20 i te 54, ka 34.

$$-0.4x+\frac{34}{15}=x-5$$

Tangohia te x mai i ngā taha e rua.

$$-0.4x+\frac{34}{15}-x=-5$$

Pahekotia te -0.4x me -x, ka -1.4x.

$$-1.4x+\frac{34}{15}=-5$$

Tangohia te \frac{34}{15} mai i ngā taha e rua.

$$-1.4x=-5-\frac{34}{15}$$

Me tahuri te -5 ki te hautau -\frac{75}{15}.

$$-1.4x=-\frac{75}{15}-\frac{34}{15}$$

Tā te mea he rite te tauraro o -\frac{75}{15} me \frac{34}{15}, me tango rāua mā te tango i ō raua taurunga.

$$-1.4x=\frac{-75-34}{15}$$

Tangohia te 34 i te -75, ka -109.

$$-1.4x=-\frac{109}{15}$$

Whakawehea ngā taha e rua ki te -1.4.

$$x=\frac{-\frac{109}{15}}{-1.4}$$

Tuhia te \frac{-\frac{109}{15}}{-1.4} hei hautanga kotahi.

$$x=\frac{-109}{15\left(-1.4\right)}$$

Whakareatia te 15 ki te -1.4, ka -21.

$$x=\frac{-109}{-21}$$

Ka taea te hautanga \frac{-109}{-21} te whakamāmā ki te \frac{109}{21} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{109}{21}$$