Whakaoti i te 2x-1/9-x-4/5=x

$$\frac{ 2x-1 }{ 9 } - \frac{ x-4 }{ 5 } =x$$

Whakaoti mō x

$$x=\frac{31}{44}\approx 0.704545455$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 9 me 5 ko 45. Whakareatia \frac{2x-1}{9} ki te \frac{5}{5}. Whakareatia \frac{x-4}{5} ki te \frac{9}{9}.

$$\frac{5\left(2x-1\right)}{45}-\frac{9\left(x-4\right)}{45}=x$$

Tā te mea he rite te tauraro o \frac{5\left(2x-1\right)}{45} me \frac{9\left(x-4\right)}{45}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{5\left(2x-1\right)-9\left(x-4\right)}{45}=x$$

Mahia ngā whakarea i roto o 5\left(2x-1\right)-9\left(x-4\right).

$$\frac{10x-5-9x+36}{45}=x$$

Whakakotahitia ngā kupu rite i 10x-5-9x+36.

$$\frac{x+31}{45}=x$$

Whakawehea ia wā o x+31 ki te 45, kia riro ko \frac{1}{45}x+\frac{31}{45}.

$$\frac{1}{45}x+\frac{31}{45}=x$$

Tangohia te x mai i ngā taha e rua.

$$\frac{1}{45}x+\frac{31}{45}-x=0$$

Pahekotia te \frac{1}{45}x me -x, ka -\frac{44}{45}x.

$$-\frac{44}{45}x+\frac{31}{45}=0$$

Tangohia te \frac{31}{45} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-\frac{44}{45}x=-\frac{31}{45}$$

Me whakarea ngā taha e rua ki te -\frac{45}{44}, te tau utu o -\frac{44}{45}.

$$x=-\frac{31}{45}\left(-\frac{45}{44}\right)$$

Me whakarea te -\frac{31}{45} ki te -\frac{45}{44} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-31\left(-45\right)}{45\times 44}$$

Mahia ngā whakarea i roto i te hautanga \frac{-31\left(-45\right)}{45\times 44}.

$$x=\frac{1395}{1980}$$

Whakahekea te hautanga \frac{1395}{1980} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 45.

$$x=\frac{31}{44}$$