Whakaoti i te 2/5(2-x)=7/4(x-4)

$$\frac { 2 } { 5 } ( 2 - x ) = \frac { 7 } { 4 } ( x - 4 )$$

Whakaoti mō x

$$x = \frac{156}{43} = 3\frac{27}{43} \approx 3.627906977$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{2}{5} ki te 2-x.

$$\frac{2}{5}\times 2+\frac{2}{5}\left(-1\right)x=\frac{7}{4}\left(x-4\right)$$

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

$$\frac{2\times 2}{5}+\frac{2}{5}\left(-1\right)x=\frac{7}{4}\left(x-4\right)$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{4}{5}+\frac{2}{5}\left(-1\right)x=\frac{7}{4}\left(x-4\right)$$

Whakareatia te \frac{2}{5} ki te -1, ka -\frac{2}{5}.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}\left(x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{7}{4} ki te x-4.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}x+\frac{7}{4}\left(-4\right)$$

Tuhia te \frac{7}{4}\left(-4\right) hei hautanga kotahi.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}x+\frac{7\left(-4\right)}{4}$$

Whakareatia te 7 ki te -4, ka -28.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}x+\frac{-28}{4}$$

Whakawehea te -28 ki te 4, kia riro ko -7.

$$\frac{4}{5}-\frac{2}{5}x=\frac{7}{4}x-7$$

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

$$\frac{4}{5}-\frac{2}{5}x-\frac{7}{4}x=-7$$

Pahekotia te -\frac{2}{5}x me -\frac{7}{4}x, ka -\frac{43}{20}x.

$$\frac{4}{5}-\frac{43}{20}x=-7$$

Tangohia te \frac{4}{5} mai i ngā taha e rua.

$$-\frac{43}{20}x=-7-\frac{4}{5}$$

Me tahuri te -7 ki te hautau -\frac{35}{5}.

$$-\frac{43}{20}x=-\frac{35}{5}-\frac{4}{5}$$

Tā te mea he rite te tauraro o -\frac{35}{5} me \frac{4}{5}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{43}{20}x=\frac{-35-4}{5}$$

Tangohia te 4 i te -35, ka -39.

$$-\frac{43}{20}x=-\frac{39}{5}$$

Me whakarea ngā taha e rua ki te -\frac{20}{43}, te tau utu o -\frac{43}{20}.

$$x=-\frac{39}{5}\left(-\frac{20}{43}\right)$$

Me whakarea te -\frac{39}{5} ki te -\frac{20}{43} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-39\left(-20\right)}{5\times 43}$$

Mahia ngā whakarea i roto i te hautanga \frac{-39\left(-20\right)}{5\times 43}.

$$x=\frac{780}{215}$$

Whakahekea te hautanga \frac{780}{215} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x=\frac{156}{43}$$