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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Add 1 and \frac{1}{2} to get \frac{3}{2}.

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

Add \frac{3}{2} and \frac{1}{3} to get \frac{11}{6}.

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

Subtract \frac{1}{3} from \frac{1}{2} to get \frac{1}{6}.

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

Use the distributive property to multiply \frac{11}{6} by \frac{x-2}{\frac{1}{6}}+1.

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

Calculate 2 to the power of -1 and get \frac{1}{2}.

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

Add 1 and \frac{1}{2} to get \frac{3}{2}.

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

Calculate 3 to the power of -1 and get \frac{1}{3}.

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

Add \frac{3}{2} and \frac{1}{3} to get \frac{11}{6}.

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

Divide each term of x-2 by \frac{1}{6} to get \frac{x}{\frac{1}{6}}+\frac{-2}{\frac{1}{6}}.

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

Divide -2 by \frac{1}{6} by multiplying -2 by the reciprocal of \frac{1}{6}.

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

Multiply -2 and 6 to get -12.

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

Use the distributive property to multiply \frac{11}{6} by \frac{x}{\frac{1}{6}}-12.

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

Add -22 and \frac{11}{6} to get -\frac{121}{6}.

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

Add \frac{121}{6} to both sides.

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

Add \frac{11}{6} and \frac{121}{6} to get 22.

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

Multiply both sides by \frac{6}{11}, the reciprocal of \frac{11}{6}.

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

Multiply 22 and \frac{6}{11} to get 12.

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

Multiply both sides by \frac{1}{6}.

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

Multiply 12 and \frac{1}{6} to get 2.

$$x=2$$