Solve for x n=(2x+1)/2

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

Rewrite the equation as $\frac{2 x + 1}{2} = n$ .

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

Multiply both sides by $2$ .

$\frac{2 x + 1}{2} \cdot 2 = n \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x + 1}{2} \cdot 2 = n \cdot 2$

Rewrite the expression.

$2 x + 1 = n \cdot 2$

$2 x + 1 = n \cdot 2$

$2 x + 1 = n \cdot 2$

Simplify the right side.

Move $2$ to the left of $n$ .

$2 x + 1 = 2 n$

$2 x + 1 = 2 n$

$2 x + 1 = 2 n$

Solve for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = 2 n - 1$

Divide each term in $2 x = 2 n - 1$ by $2$ and simplify.

Divide each term in $2 x = 2 n - 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

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

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $n$ by $1$ .

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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