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

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

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

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

Cancel out \frac{2}{3} and its reciprocal \frac{3}{2}.

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

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

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

Express -\frac{1}{2}\left(-3\right) as a single fraction.

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

Multiply -1 and -3 to get 3.

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

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

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

Add \frac{1}{2} to both sides.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

$$3x=\frac{3}{2}$$

Divide both sides by 3.

$$x=\frac{\frac{3}{2}}{3}$$

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

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

Cancel out 3 in both numerator and denominator.

$$x=\frac{1}{2}$$