Atrisiniet (1+1/2+1/3)(x-2/frac{1{2}-1/3}+1)=1+2^-1+3^-1

$$( 1 + \frac { 1 } { 2 } + \frac { 1 } { 3 } ) ( \frac { x - 2 } { \frac { 1 } { 2 } - \frac { 1 } { 3 } } + 1 ) = 1 + 2 ^ { - 1 } + 3 ^ { - 1 }$$

Atrast x

$$x=2$$

Lineāra vienādojuma risināšanas darbības

Saskaitiet 1 un \frac{1}{2}, lai iegūtu \frac{3}{2}.

$$\left(\frac{3}{2}+\frac{1}{3}\right)\left(\frac{x-2}{\frac{1}{2}-\frac{1}{3}}+1\right)=1+2^{-1}+3^{-1}$$

Saskaitiet \frac{3}{2} un \frac{1}{3}, lai iegūtu \frac{11}{6}.

$$\frac{11}{6}\left(\frac{x-2}{\frac{1}{2}-\frac{1}{3}}+1\right)=1+2^{-1}+3^{-1}$$

Atņemiet \frac{1}{3} no \frac{1}{2}, lai iegūtu \frac{1}{6}.

$$\frac{11}{6}\left(\frac{x-2}{\frac{1}{6}}+1\right)=1+2^{-1}+3^{-1}$$

Izmantojiet distributīvo īpašību, lai reizinātu \frac{11}{6} ar \frac{x-2}{\frac{1}{6}}+1.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=1+2^{-1}+3^{-1}$$

Aprēķiniet 2 pakāpē -1 un iegūstiet \frac{1}{2}.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=1+\frac{1}{2}+3^{-1}$$

Saskaitiet 1 un \frac{1}{2}, lai iegūtu \frac{3}{2}.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{3}{2}+3^{-1}$$

Aprēķiniet 3 pakāpē -1 un iegūstiet \frac{1}{3}.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{3}{2}+\frac{1}{3}$$

Saskaitiet \frac{3}{2} un \frac{1}{3}, lai iegūtu \frac{11}{6}.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{11}{6}$$

Daliet katru x-2 locekli ar \frac{1}{6}, lai iegūtu \frac{x}{\frac{1}{6}}+\frac{-2}{\frac{1}{6}}.

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}+\frac{-2}{\frac{1}{6}}\right)+\frac{11}{6}=\frac{11}{6}$$

Daliet -2 ar \frac{1}{6}, reizinot -2 ar apgriezto daļskaitli \frac{1}{6} .

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}-2\times 6\right)+\frac{11}{6}=\frac{11}{6}$$

Reiziniet -2 un 6, lai iegūtu -12.

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}-12\right)+\frac{11}{6}=\frac{11}{6}$$

Izmantojiet distributīvo īpašību, lai reizinātu \frac{11}{6} ar \frac{x}{\frac{1}{6}}-12.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}-22+\frac{11}{6}=\frac{11}{6}$$

Saskaitiet -22 un \frac{11}{6}, lai iegūtu -\frac{121}{6}.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}-\frac{121}{6}=\frac{11}{6}$$

Pievienot \frac{121}{6} abās pusēs.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}=\frac{11}{6}+\frac{121}{6}$$

Saskaitiet \frac{11}{6} un \frac{121}{6}, lai iegūtu 22.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}=22$$

Reiziniet abās puses ar \frac{6}{11}, abpusēju \frac{11}{6} vērtību.

$$\frac{x}{\frac{1}{6}}=22\times \frac{6}{11}$$

Reiziniet 22 un \frac{6}{11}, lai iegūtu 12.

$$\frac{x}{\frac{1}{6}}=12$$

Reiziniet abas puses ar \frac{1}{6}.

$$x=12\times \frac{1}{6}$$

Reiziniet 12 un \frac{1}{6}, lai iegūtu 2.

$$x=2$$