Solve 1/4(2x-x-7/3)-1/2(x-2x+1/3)=frac{x}{2}

$$\frac { 1 } { 4 } ( 2 x - \frac { x - 7 } { 3 } ) - \frac { 1 } { 2 } ( x - \frac { 2 x + 1 } { 3 } ) = \frac { x } { 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3,2.

$$3\left(2x-\frac{x-7}{3}\right)-6\left(x-\frac{2x+1}{3}\right)=6x$$

Use the distributive property to multiply 3 by 2x-\frac{x-7}{3}.

$$6x+3\left(-\frac{x-7}{3}\right)-6\left(x-\frac{2x+1}{3}\right)=6x$$

Express 3\left(-\frac{x-7}{3}\right) as a single fraction.

$$6x+\frac{-3\left(x-7\right)}{3}-6\left(x-\frac{2x+1}{3}\right)=6x$$

Cancel out 3 and 3.

$$6x-\left(x-7\right)-6\left(x-\frac{2x+1}{3}\right)=6x$$

To find the opposite of x-7, find the opposite of each term.

$$6x-x-\left(-7\right)-6\left(x-\frac{2x+1}{3}\right)=6x$$

The opposite of -7 is 7.

$$6x-x+7-6\left(x-\frac{2x+1}{3}\right)=6x$$

Combine 6x and -x to get 5x.

$$5x+7-6\left(x-\frac{2x+1}{3}\right)=6x$$

Divide each term of 2x+1 by 3 to get \frac{2}{3}x+\frac{1}{3}.

$$5x+7-6\left(x-\left(\frac{2}{3}x+\frac{1}{3}\right)\right)=6x$$

To find the opposite of \frac{2}{3}x+\frac{1}{3}, find the opposite of each term.

$$5x+7-6\left(x-\frac{2}{3}x-\frac{1}{3}\right)=6x$$

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

$$5x+7-6\left(\frac{1}{3}x-\frac{1}{3}\right)=6x$$

Use the distributive property to multiply -6 by \frac{1}{3}x-\frac{1}{3}.

$$5x+7-6\times \frac{1}{3}x-6\left(-\frac{1}{3}\right)=6x$$

Multiply -6 and \frac{1}{3} to get \frac{-6}{3}.

$$5x+7+\frac{-6}{3}x-6\left(-\frac{1}{3}\right)=6x$$

Divide -6 by 3 to get -2.

$$5x+7-2x-6\left(-\frac{1}{3}\right)=6x$$

Express -6\left(-\frac{1}{3}\right) as a single fraction.

$$5x+7-2x+\frac{-6\left(-1\right)}{3}=6x$$

Multiply -6 and -1 to get 6.

$$5x+7-2x+\frac{6}{3}=6x$$

Divide 6 by 3 to get 2.

$$5x+7-2x+2=6x$$

Combine 5x and -2x to get 3x.

$$3x+7+2=6x$$

Add 7 and 2 to get 9.

$$3x+9=6x$$

Subtract 6x from both sides.

$$3x+9-6x=0$$

Combine 3x and -6x to get -3x.

$$-3x+9=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-9$$

Divide both sides by -3.

$$x=\frac{-9}{-3}$$

Divide -9 by -3 to get 3.

$$x=3$$