Whakaoti i te 5/6(2x+14)=7/12(3x+20)

$$\frac { 5 } { 6 } ( 2 x + 14 ) = \frac { 7 } { 12 } ( 3 x + 20 )$$

Whakaoti mō x

$$x=0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{5}{6} ki te 2x+14.

$$\frac{5}{6}\times 2x+\frac{5}{6}\times 14=\frac{7}{12}\left(3x+20\right)$$

Tuhia te \frac{5}{6}\times 2 hei hautanga kotahi.

$$\frac{5\times 2}{6}x+\frac{5}{6}\times 14=\frac{7}{12}\left(3x+20\right)$$

Whakareatia te 5 ki te 2, ka 10.

$$\frac{10}{6}x+\frac{5}{6}\times 14=\frac{7}{12}\left(3x+20\right)$$

Whakahekea te hautanga \frac{10}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{5}{3}x+\frac{5}{6}\times 14=\frac{7}{12}\left(3x+20\right)$$

Tuhia te \frac{5}{6}\times 14 hei hautanga kotahi.

$$\frac{5}{3}x+\frac{5\times 14}{6}=\frac{7}{12}\left(3x+20\right)$$

Whakareatia te 5 ki te 14, ka 70.

$$\frac{5}{3}x+\frac{70}{6}=\frac{7}{12}\left(3x+20\right)$$

Whakahekea te hautanga \frac{70}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{12}\left(3x+20\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{7}{12} ki te 3x+20.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{12}\times 3x+\frac{7}{12}\times 20$$

Tuhia te \frac{7}{12}\times 3 hei hautanga kotahi.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7\times 3}{12}x+\frac{7}{12}\times 20$$

Whakareatia te 7 ki te 3, ka 21.

$$\frac{5}{3}x+\frac{35}{3}=\frac{21}{12}x+\frac{7}{12}\times 20$$

Whakahekea te hautanga \frac{21}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{4}x+\frac{7}{12}\times 20$$

Tuhia te \frac{7}{12}\times 20 hei hautanga kotahi.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{4}x+\frac{7\times 20}{12}$$

Whakareatia te 7 ki te 20, ka 140.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{4}x+\frac{140}{12}$$

Whakahekea te hautanga \frac{140}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{4}x+\frac{35}{3}$$

Tangohia te \frac{7}{4}x mai i ngā taha e rua.

$$\frac{5}{3}x+\frac{35}{3}-\frac{7}{4}x=\frac{35}{3}$$

Pahekotia te \frac{5}{3}x me -\frac{7}{4}x, ka -\frac{1}{12}x.

$$-\frac{1}{12}x+\frac{35}{3}=\frac{35}{3}$$

Tangohia te \frac{35}{3} mai i ngā taha e rua.

$$-\frac{1}{12}x=\frac{35}{3}-\frac{35}{3}$$

Tangohia te \frac{35}{3} i te \frac{35}{3}, ka 0.

$$-\frac{1}{12}x=0$$

He ōrite te hua o ngā tau e rua ki 0 ina 0 tētahi o rāua te iti rawa. Tātemea kāore te -\frac{1}{12} e ōrite ki 0, me ōrite pū te x ki 0.

$$x=0$$