Whakaoti i te 1/4(3x+5)=1/3(5x-4)

$$\frac { 1 } { 4 } ( 3 x + 5 ) = \frac { 1 } { 3 } ( 5 x - 4 )$$

Whakaoti mō x

$$x = \frac{31}{11} = 2\frac{9}{11} \approx 2.818181818$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{4} ki te 3x+5.

$$\frac{1}{4}\times 3x+\frac{1}{4}\times 5=\frac{1}{3}\left(5x-4\right)$$

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

$$\frac{3}{4}x+\frac{1}{4}\times 5=\frac{1}{3}\left(5x-4\right)$$

Whakareatia te \frac{1}{4} ki te 5, ka \frac{5}{4}.

$$\frac{3}{4}x+\frac{5}{4}=\frac{1}{3}\left(5x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{3} ki te 5x-4.

$$\frac{3}{4}x+\frac{5}{4}=\frac{1}{3}\times 5x+\frac{1}{3}\left(-4\right)$$

Whakareatia te \frac{1}{3} ki te 5, ka \frac{5}{3}.

$$\frac{3}{4}x+\frac{5}{4}=\frac{5}{3}x+\frac{1}{3}\left(-4\right)$$

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

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

Ka taea te hautanga \frac{-4}{3} te tuhi anō ko -\frac{4}{3} mā te tango i te tohu tōraro.

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

Tangohia te \frac{5}{3}x mai i ngā taha e rua.

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

Pahekotia te \frac{3}{4}x me -\frac{5}{3}x, ka -\frac{11}{12}x.

$$-\frac{11}{12}x+\frac{5}{4}=-\frac{4}{3}$$

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

$$-\frac{11}{12}x=-\frac{4}{3}-\frac{5}{4}$$

Ko te maha noa iti rawa atu o 3 me 4 ko 12. Me tahuri -\frac{4}{3} me \frac{5}{4} ki te hautau me te tautūnga 12.

$$-\frac{11}{12}x=-\frac{16}{12}-\frac{15}{12}$$

Tā te mea he rite te tauraro o -\frac{16}{12} me \frac{15}{12}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{11}{12}x=\frac{-16-15}{12}$$

Tangohia te 15 i te -16, ka -31.

$$-\frac{11}{12}x=-\frac{31}{12}$$

Me whakarea ngā taha e rua ki te -\frac{12}{11}, te tau utu o -\frac{11}{12}.

$$x=-\frac{31}{12}\left(-\frac{12}{11}\right)$$

Me whakarea te -\frac{31}{12} ki te -\frac{12}{11} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-31\left(-12\right)}{12\times 11}$$

Mahia ngā whakarea i roto i te hautanga \frac{-31\left(-12\right)}{12\times 11}.

$$x=\frac{372}{132}$$

Whakahekea te hautanga \frac{372}{132} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$x=\frac{31}{11}$$