Whakaoti i te 17/30(x+3)=17/50(x+10)

$$\frac { 17 } { 30 } ( x + 3 ) = \frac { 17 } { 50 } ( x + 10 )$$

Whakaoti mō x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{17}{30} ki te x+3.

$$\frac{17}{30}x+\frac{17}{30}\times 3=\frac{17}{50}\left(x+10\right)$$

Tuhia te \frac{17}{30}\times 3 hei hautanga kotahi.

$$\frac{17}{30}x+\frac{17\times 3}{30}=\frac{17}{50}\left(x+10\right)$$

Whakareatia te 17 ki te 3, ka 51.

$$\frac{17}{30}x+\frac{51}{30}=\frac{17}{50}\left(x+10\right)$$

Whakahekea te hautanga \frac{51}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}\left(x+10\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{17}{50} ki te x+10.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}x+\frac{17}{50}\times 10$$

Tuhia te \frac{17}{50}\times 10 hei hautanga kotahi.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}x+\frac{17\times 10}{50}$$

Whakareatia te 17 ki te 10, ka 170.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}x+\frac{170}{50}$$

Whakahekea te hautanga \frac{170}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}x+\frac{17}{5}$$

Tangohia te \frac{17}{50}x mai i ngā taha e rua.

$$\frac{17}{30}x+\frac{17}{10}-\frac{17}{50}x=\frac{17}{5}$$

Pahekotia te \frac{17}{30}x me -\frac{17}{50}x, ka \frac{17}{75}x.

$$\frac{17}{75}x+\frac{17}{10}=\frac{17}{5}$$

Tangohia te \frac{17}{10} mai i ngā taha e rua.

$$\frac{17}{75}x=\frac{17}{5}-\frac{17}{10}$$

Ko te maha noa iti rawa atu o 5 me 10 ko 10. Me tahuri \frac{17}{5} me \frac{17}{10} ki te hautau me te tautūnga 10.

$$\frac{17}{75}x=\frac{34}{10}-\frac{17}{10}$$

Tā te mea he rite te tauraro o \frac{34}{10} me \frac{17}{10}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{17}{75}x=\frac{34-17}{10}$$

Tangohia te 17 i te 34, ka 17.

$$\frac{17}{75}x=\frac{17}{10}$$

Me whakarea ngā taha e rua ki te \frac{75}{17}, te tau utu o \frac{17}{75}.

$$x=\frac{17}{10}\times \frac{75}{17}$$

Me whakarea te \frac{17}{10} ki te \frac{75}{17} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{17\times 75}{10\times 17}$$

Me whakakore tahi te 17 i te taurunga me te tauraro.

$$x=\frac{75}{10}$$

Whakahekea te hautanga \frac{75}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x=\frac{15}{2}$$