Whakaoti i te 75%(x-1)-25%(x-4)=25%(x+6)

$$75 \% ( x - 1 ) - 25 \% ( x - 4 ) = 25 \% ( x + 6 )$$

Whakaoti mō x

$$x=5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{75}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\frac{3}{4}\left(x-1\right)-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4} ki te x-1.

$$\frac{3}{4}x+\frac{3}{4}\left(-1\right)-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

Whakareatia te \frac{3}{4} ki te -1, ka -\frac{3}{4}.

$$\frac{3}{4}x-\frac{3}{4}-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

Whakahekea te hautanga \frac{25}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{4} ki te x-4.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x-\frac{1}{4}\left(-4\right)=\frac{25}{100}\left(x+6\right)$$

Tuhia te -\frac{1}{4}\left(-4\right) hei hautanga kotahi.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+\frac{-\left(-4\right)}{4}=\frac{25}{100}\left(x+6\right)$$

Whakareatia te -1 ki te -4, ka 4.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+\frac{4}{4}=\frac{25}{100}\left(x+6\right)$$

Whakawehea te 4 ki te 4, kia riro ko 1.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+1=\frac{25}{100}\left(x+6\right)$$

Pahekotia te \frac{3}{4}x me -\frac{1}{4}x, ka \frac{1}{2}x.

$$\frac{1}{2}x-\frac{3}{4}+1=\frac{25}{100}\left(x+6\right)$$

Me tahuri te 1 ki te hautau \frac{4}{4}.

$$\frac{1}{2}x-\frac{3}{4}+\frac{4}{4}=\frac{25}{100}\left(x+6\right)$$

Tā te mea he rite te tauraro o -\frac{3}{4} me \frac{4}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{2}x+\frac{-3+4}{4}=\frac{25}{100}\left(x+6\right)$$

Tāpirihia te -3 ki te 4, ka 1.

$$\frac{1}{2}x+\frac{1}{4}=\frac{25}{100}\left(x+6\right)$$

Whakahekea te hautanga \frac{25}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te x+6.

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}x+\frac{1}{4}\times 6$$

Whakareatia te \frac{1}{4} ki te 6, ka \frac{6}{4}.

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}x+\frac{6}{4}$$

Whakahekea te hautanga \frac{6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}x+\frac{3}{2}$$

Tangohia te \frac{1}{4}x mai i ngā taha e rua.

$$\frac{1}{2}x+\frac{1}{4}-\frac{1}{4}x=\frac{3}{2}$$

Pahekotia te \frac{1}{2}x me -\frac{1}{4}x, ka \frac{1}{4}x.

$$\frac{1}{4}x+\frac{1}{4}=\frac{3}{2}$$

Tangohia te \frac{1}{4} mai i ngā taha e rua.

$$\frac{1}{4}x=\frac{3}{2}-\frac{1}{4}$$

Ko te maha noa iti rawa atu o 2 me 4 ko 4. Me tahuri \frac{3}{2} me \frac{1}{4} ki te hautau me te tautūnga 4.

$$\frac{1}{4}x=\frac{6}{4}-\frac{1}{4}$$

Tā te mea he rite te tauraro o \frac{6}{4} me \frac{1}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{4}x=\frac{6-1}{4}$$

Tangohia te 1 i te 6, ka 5.

$$\frac{1}{4}x=\frac{5}{4}$$

Me whakarea ngā taha e rua ki te 4, te tau utu o \frac{1}{4}.

$$x=\frac{5}{4}\times 4$$

Me whakakore te 4 me te 4.

$$x=5$$