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

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

Resolva para x

$$x=2$$

Passos Para Resolver Uma Equação Linear

Some 1 e \frac{1}{2} para obter \frac{3}{2}.

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

Some \frac{3}{2} e \frac{1}{3} para obter \frac{11}{6}.

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

Subtraia \frac{1}{3} de \frac{1}{2} para obter \frac{1}{6}.

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

Utilize a propriedade distributiva para multiplicar \frac{11}{6} por \frac{x-2}{\frac{1}{6}}+1.

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

Calcule 2 elevado a -1 e obtenha \frac{1}{2}.

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

Some 1 e \frac{1}{2} para obter \frac{3}{2}.

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

Calcule 3 elevado a -1 e obtenha \frac{1}{3}.

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

Some \frac{3}{2} e \frac{1}{3} para obter \frac{11}{6}.

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

Divida cada termo de x-2 por \frac{1}{6} para obter \frac{x}{\frac{1}{6}}+\frac{-2}{\frac{1}{6}}.

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

Divida -2 por \frac{1}{6} ao multiplicar -2 pelo recíproco de \frac{1}{6}.

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

Multiplique -2 e 6 para obter -12.

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

Utilize a propriedade distributiva para multiplicar \frac{11}{6} por \frac{x}{\frac{1}{6}}-12.

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

Some -22 e \frac{11}{6} para obter -\frac{121}{6}.

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

Adicionar \frac{121}{6} em ambos os lados.

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

Some \frac{11}{6} e \frac{121}{6} para obter 22.

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

Multiplique ambos os lados por \frac{6}{11}, o recíproco de \frac{11}{6}.

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

Multiplique 22 e \frac{6}{11} para obter 12.

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

Multiplique ambos os lados por \frac{1}{6}.

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

Multiplique 12 e \frac{1}{6} para obter 2.

$$x=2$$