Solve 1/2[x+1/3(2-x)]=2/3(x+2)

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

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 2-x.

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

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

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

Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.

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

Combine x and -\frac{1}{3}x to get \frac{2}{3}x.

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

Use the distributive property to multiply \frac{1}{2} by \frac{2}{3}x+\frac{2}{3}.

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

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Use the distributive property to multiply \frac{2}{3} by x+2.

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

Express \frac{2}{3}\times 2 as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Subtract \frac{2}{3}x from both sides.

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

Combine \frac{1}{3}x and -\frac{2}{3}x to get -\frac{1}{3}x.

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

Subtract \frac{1}{3} from both sides.

$$-\frac{1}{3}x=\frac{4}{3}-\frac{1}{3}$$

Since \frac{4}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}x=\frac{4-1}{3}$$

Subtract 1 from 4 to get 3.

$$-\frac{1}{3}x=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$-\frac{1}{3}x=1$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=1\left(-3\right)$$

Multiply 1 and -3 to get -3.

$$x=-3$$