Whakaoti i te 7x-1/0.024=1-0.2x/0.018-5x+1/0.012

$$\frac { 7 x - 1 } { 0.024 } = \frac { 1 - 0.2 x } { 0.018 } - \frac { 5 x + 1 } { 0.012 }$$

Whakaoti mō x

$$x=\frac{5}{259}\approx 0.019305019$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawehea ia wā o 7x-1 ki te 0.024, kia riro ko \frac{7x}{0.024}+\frac{-1}{0.024}.

$$\frac{7x}{0.024}+\frac{-1}{0.024}=\frac{1-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Whakawehea te 7x ki te 0.024, kia riro ko \frac{875}{3}x.

$$\frac{875}{3}x+\frac{-1}{0.024}=\frac{1-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Whakarohaina te \frac{-1}{0.024} mā te whakarea i te taurunga me te tauraro ki te 1000.

$$\frac{875}{3}x+\frac{-1000}{24}=\frac{1-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Whakahekea te hautanga \frac{-1000}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$\frac{875}{3}x-\frac{125}{3}=\frac{1-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Whakawehea ia wā o 1-0.2x ki te 0.018, kia riro ko \frac{1}{0.018}+\frac{-0.2x}{0.018}.

$$\frac{875}{3}x-\frac{125}{3}=\frac{1}{0.018}+\frac{-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Whakarohaina te \frac{1}{0.018} mā te whakarea i te taurunga me te tauraro ki te 1000.

$$\frac{875}{3}x-\frac{125}{3}=\frac{1000}{18}+\frac{-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Whakahekea te hautanga \frac{1000}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}+\frac{-0.2x}{0.018}-\frac{5x+1}{0.012}$$

Whakawehea te -0.2x ki te 0.018, kia riro ko -\frac{100}{9}x.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\frac{5x+1}{0.012}$$

Whakawehea ia wā o 5x+1 ki te 0.012, kia riro ko \frac{5x}{0.012}+\frac{1}{0.012}.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\left(\frac{5x}{0.012}+\frac{1}{0.012}\right)$$

Whakawehea te 5x ki te 0.012, kia riro ko \frac{1250}{3}x.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\left(\frac{1250}{3}x+\frac{1}{0.012}\right)$$

Whakarohaina te \frac{1}{0.012} mā te whakarea i te taurunga me te tauraro ki te 1000.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\left(\frac{1250}{3}x+\frac{1000}{12}\right)$$

Whakahekea te hautanga \frac{1000}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\left(\frac{1250}{3}x+\frac{250}{3}\right)$$

Hei kimi i te tauaro o \frac{1250}{3}x+\frac{250}{3}, kimihia te tauaro o ia taurangi.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{100}{9}x-\frac{1250}{3}x-\frac{250}{3}$$

Pahekotia te -\frac{100}{9}x me -\frac{1250}{3}x, ka -\frac{3850}{9}x.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{3850}{9}x-\frac{250}{3}$$

Ko te maha noa iti rawa atu o 9 me 3 ko 9. Me tahuri \frac{500}{9} me \frac{250}{3} ki te hautau me te tautūnga 9.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500}{9}-\frac{3850}{9}x-\frac{750}{9}$$

Tā te mea he rite te tauraro o \frac{500}{9} me \frac{750}{9}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{875}{3}x-\frac{125}{3}=\frac{500-750}{9}-\frac{3850}{9}x$$

Tangohia te 750 i te 500, ka -250.

$$\frac{875}{3}x-\frac{125}{3}=-\frac{250}{9}-\frac{3850}{9}x$$

Me tāpiri te \frac{3850}{9}x ki ngā taha e rua.

$$\frac{875}{3}x-\frac{125}{3}+\frac{3850}{9}x=-\frac{250}{9}$$

Pahekotia te \frac{875}{3}x me \frac{3850}{9}x, ka \frac{6475}{9}x.

$$\frac{6475}{9}x-\frac{125}{3}=-\frac{250}{9}$$

Me tāpiri te \frac{125}{3} ki ngā taha e rua.

$$\frac{6475}{9}x=-\frac{250}{9}+\frac{125}{3}$$

Ko te maha noa iti rawa atu o 9 me 3 ko 9. Me tahuri -\frac{250}{9} me \frac{125}{3} ki te hautau me te tautūnga 9.

$$\frac{6475}{9}x=-\frac{250}{9}+\frac{375}{9}$$

Tā te mea he rite te tauraro o -\frac{250}{9} me \frac{375}{9}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{6475}{9}x=\frac{-250+375}{9}$$

Tāpirihia te -250 ki te 375, ka 125.

$$\frac{6475}{9}x=\frac{125}{9}$$

Whakawehea ngā taha e rua ki te \frac{6475}{9}.

$$x=\frac{\frac{125}{9}}{\frac{6475}{9}}$$

Tuhia te \frac{\frac{125}{9}}{\frac{6475}{9}} hei hautanga kotahi.

$$x=\frac{125}{9\times \frac{6475}{9}}$$

Whakareatia te 9 ki te \frac{6475}{9}, ka 6475.

$$x=\frac{125}{6475}$$

Whakahekea te hautanga \frac{125}{6475} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$x=\frac{5}{259}$$