Whakaoti i te 0.9x-0.5x-200=0.9x0.2%

$$0.9x-0.5x-200 = 0.9x0.2 \%$$

Whakaoti mō x

$$x = \frac{1000000}{1991} = 502\frac{518}{1991} \approx 502.260170768$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pahekotia te 0.9x me -0.5x, ka 0.4x.

$$0.4x-200=0.9x\times \frac{0.2}{100}$$

Whakarohaina te \frac{0.2}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$0.4x-200=0.9x\times \frac{2}{1000}$$

Whakahekea te hautanga \frac{2}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$0.4x-200=0.9x\times \frac{1}{500}$$

Me tahuri ki tau ā-ira 0.9 ki te hautau \frac{9}{10}.

$$0.4x-200=\frac{9}{10}x\times \frac{1}{500}$$

Me whakarea te \frac{9}{10} ki te \frac{1}{500} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$0.4x-200=\frac{9\times 1}{10\times 500}x$$

Mahia ngā whakarea i roto i te hautanga \frac{9\times 1}{10\times 500}.

$$0.4x-200=\frac{9}{5000}x$$

Tangohia te \frac{9}{5000}x mai i ngā taha e rua.

$$0.4x-200-\frac{9}{5000}x=0$$

Pahekotia te 0.4x me -\frac{9}{5000}x, ka \frac{1991}{5000}x.

$$\frac{1991}{5000}x-200=0$$

Me tāpiri te 200 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$\frac{1991}{5000}x=200$$

Me whakarea ngā taha e rua ki te \frac{5000}{1991}, te tau utu o \frac{1991}{5000}.

$$x=200\times \frac{5000}{1991}$$

Tuhia te 200\times \frac{5000}{1991} hei hautanga kotahi.

$$x=\frac{200\times 5000}{1991}$$

Whakareatia te 200 ki te 5000, ka 1000000.

$$x=\frac{1000000}{1991}$$