Whakaoti i te (3/4x+1/3)*1/2=2x+1

$$( \frac { 3 } { 4 } x + \frac { 1 } { 3 } ) \times \frac { 1 } { 2 } = 2 x + 1$$

Whakaoti mō x

$$x=-\frac{20}{39}\approx -0.512820513$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4}x+\frac{1}{3} ki te \frac{1}{2}.

$$\frac{3}{4}x\times \frac{1}{2}+\frac{1}{3}\times \frac{1}{2}=2x+1$$

Me whakarea te \frac{3}{4} ki te \frac{1}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{3\times 1}{4\times 2}x+\frac{1}{3}\times \frac{1}{2}=2x+1$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 1}{4\times 2}.

$$\frac{3}{8}x+\frac{1}{3}\times \frac{1}{2}=2x+1$$

Me whakarea te \frac{1}{3} ki te \frac{1}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{3}{8}x+\frac{1\times 1}{3\times 2}=2x+1$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 1}{3\times 2}.

$$\frac{3}{8}x+\frac{1}{6}=2x+1$$

Tangohia te 2x mai i ngā taha e rua.

$$\frac{3}{8}x+\frac{1}{6}-2x=1$$

Pahekotia te \frac{3}{8}x me -2x, ka -\frac{13}{8}x.

$$-\frac{13}{8}x+\frac{1}{6}=1$$

Tangohia te \frac{1}{6} mai i ngā taha e rua.

$$-\frac{13}{8}x=1-\frac{1}{6}$$

Me tahuri te 1 ki te hautau \frac{6}{6}.

$$-\frac{13}{8}x=\frac{6}{6}-\frac{1}{6}$$

Tā te mea he rite te tauraro o \frac{6}{6} me \frac{1}{6}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{13}{8}x=\frac{6-1}{6}$$

Tangohia te 1 i te 6, ka 5.

$$-\frac{13}{8}x=\frac{5}{6}$$

Me whakarea ngā taha e rua ki te -\frac{8}{13}, te tau utu o -\frac{13}{8}.

$$x=\frac{5}{6}\left(-\frac{8}{13}\right)$$

Me whakarea te \frac{5}{6} ki te -\frac{8}{13} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{5\left(-8\right)}{6\times 13}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\left(-8\right)}{6\times 13}.

$$x=\frac{-40}{78}$$

Whakahekea te hautanga \frac{-40}{78} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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