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

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

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 3x-1.

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

Combine 6x and -x to get 5x.

$$2x-\frac{1}{3}\left(5x-2\right)=\frac{1}{2}x$$

Use the distributive property to multiply -\frac{1}{3} by 5x-2.

$$2x-\frac{1}{3}\times 5x-\frac{1}{3}\left(-2\right)=\frac{1}{2}x$$

Express -\frac{1}{3}\times 5 as a single fraction.

$$2x+\frac{-5}{3}x-\frac{1}{3}\left(-2\right)=\frac{1}{2}x$$

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$2x-\frac{5}{3}x-\frac{1}{3}\left(-2\right)=\frac{1}{2}x$$

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

$$2x-\frac{5}{3}x+\frac{-\left(-2\right)}{3}=\frac{1}{2}x$$

Multiply -1 and -2 to get 2.

$$2x-\frac{5}{3}x+\frac{2}{3}=\frac{1}{2}x$$

Combine 2x and -\frac{5}{3}x to get \frac{1}{3}x.

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

Subtract \frac{1}{2}x from both sides.

$$\frac{1}{3}x+\frac{2}{3}-\frac{1}{2}x=0$$

Combine \frac{1}{3}x and -\frac{1}{2}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x+\frac{2}{3}=0$$

Subtract \frac{2}{3} from both sides. Anything subtracted from zero gives its negation.

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

Multiply both sides by -6, the reciprocal of -\frac{1}{6}.

$$x=-\frac{2}{3}\left(-6\right)$$

Express -\frac{2}{3}\left(-6\right) as a single fraction.

$$x=\frac{-2\left(-6\right)}{3}$$

Multiply -2 and -6 to get 12.

$$x=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$x=4$$