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

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{x+\frac{1}{2}}{2x-\frac{1}{2}}.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{2x+1}{\left(\frac{1}{2}\right)^{0}\left(4x-1\right)}=\frac{1}{3}$$

Calculate \frac{1}{2} to the power of 0 and get 1.

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

Use the distributive property to multiply 1 by 4x-1.

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

Variable x cannot be equal to \frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by 3\left(4x-1\right), the least common multiple of 4x-1,3.

$$3\left(2x+1\right)=4x-1$$

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

$$6x+3=4x-1$$

Subtract 4x from both sides.

$$6x+3-4x=-1$$

Combine 6x and -4x to get 2x.

$$2x+3=-1$$

Subtract 3 from both sides.

$$2x=-1-3$$

Subtract 3 from -1 to get -4.

$$2x=-4$$

Divide both sides by 2.

$$x=\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$x=-2$$