Solve for n 1/2n+7=(n+14)/2

$\frac{1}{2} n + 7 = \frac{n + 14}{2}$

Multiply both sides by $2$ .

$(\frac{1}{2} n + 7) \cdot 2 = \frac{n + 14}{2} \cdot 2$

Simplify.

Simplify the left side.

Simplify $(\frac{1}{2} n + 7) \cdot 2$ .

Combine $\frac{1}{2}$ and $n$ .

$(\frac{n}{2} + 7) \cdot 2 = \frac{n + 14}{2} \cdot 2$

Apply the distributive property.

$\frac{n}{2} \cdot 2 + 7 \cdot 2 = \frac{n + 14}{2} \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{n}{2} \cdot 2 + 7 \cdot 2 = \frac{n + 14}{2} \cdot 2$

Rewrite the expression.

$n + 7 \cdot 2 = \frac{n + 14}{2} \cdot 2$

Multiply $7$ by $2$ .

$n + 14 = \frac{n + 14}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$n + 14 = \frac{n + 14}{2} \cdot 2$

Rewrite the expression.

$n + 14 = n + 14$

Solve for $n$ .

Move all terms containing $n$ to the left side of the equation.

Subtract $n$ from both sides of the equation.

$n + 14 - n = 14$

Combine the opposite terms in $n + 14 - n$ .

Subtract $n$ from $n$ .

$0 + 14 = 14$

Add $0$ and $14$ .

$14 = 14$

Since $14 = 14$ , the equation will always be true for any value of $n$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$