Solve x+1/2/2x-frac{1{2}}=13

$$\frac { x + \frac { 1 } { 2 } } { 2 x - \frac { 1 } { 2 } } = 13$$

Solve for x

$$x=\frac{7}{25}=0.28$$

Steps for Solving Linear Equation

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

$$\frac{\frac{1}{2}\left(2x+1\right)}{\frac{1}{2}\left(4x-1\right)}=13$$

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

$$\frac{2x+1}{\left(\frac{1}{2}\right)^{0}\left(4x-1\right)}=13$$

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

$$\frac{2x+1}{1\left(4x-1\right)}=13$$

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

$$\frac{2x+1}{4x-1}=13$$

Variable x cannot be equal to \frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by 4x-1.

$$2x+1=13\left(4x-1\right)$$

Use the distributive property to multiply 13 by 4x-1.

$$2x+1=52x-13$$

Subtract 52x from both sides.

$$2x+1-52x=-13$$

Combine 2x and -52x to get -50x.

$$-50x+1=-13$$

Subtract 1 from both sides.

$$-50x=-13-1$$

Subtract 1 from -13 to get -14.

$$-50x=-14$$

Divide both sides by -50.

$$x=\frac{-14}{-50}$$

Reduce the fraction \frac{-14}{-50} to lowest terms by extracting and canceling out -2.

$$x=\frac{7}{25}$$