Solve for n 2-1/2n=3n+16

$2 - \frac{1}{2} n = 3 n + 16$

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

$2 - \frac{n}{2} = 3 n + 16$

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

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Subtract $3 n$ from both sides of the equation.

$2 - \frac{n}{2} - 3 n = 16$

Simplify the left side of the equation.

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To write $\frac{- 3 n}{1}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 - \frac{n}{2} + \frac{- 3 n}{1} \cdot \frac{2}{2} = 16$

Write each expression with a common denominator of $2$ , by multiplying each by an appropriate factor of $1$ .

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Combine.

$2 - \frac{n}{2} + \frac{- 3 n \cdot 2}{1 \cdot 2} = 16$

Multiply $2$ by $1$ .

$2 - \frac{n}{2} + \frac{- 3 n \cdot 2}{2} = 16$

Combine the numerators over the common denominator.

$2 + \frac{- n - 3 n \cdot 2}{2} = 16$

Simplify each term.

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Simplify the numerator.

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Factor $n$ out of $- n - 3 n \cdot 2$ .

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Factor $n$ out of $- n$ .

$2 + \frac{n \cdot - 1 - 3 n \cdot 2}{2} = 16$

Factor $n$ out of $- 3 n \cdot 2$ .

$2 + \frac{n \cdot - 1 + n (- 3 \cdot 2)}{2} = 16$

Factor $n$ out of $n \cdot - 1 + n (- 3 \cdot 2)$ .

$2 + \frac{n (- 1 - 3 \cdot 2)}{2} = 16$

Multiply $- 3$ by $2$ .

$2 + \frac{n (- 1 - 6)}{2} = 16$

Subtract $6$ from $- 1$ .

$2 + \frac{n \cdot - 7}{2} = 16$

Move $- 7$ to the left of $n$ .

$2 + \frac{- 7 \cdot n}{2} = 16$

Move the negative in front of the fraction.

$2 - \frac{7 n}{2} = 16$

Move all terms not containing $n$ to the right side of the equation.

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Subtract $2$ from both sides of the equation.

$- \frac{7 n}{2} = 16 - 2$

Subtract $2$ from $16$ .

$- \frac{7 n}{2} = 14$

Multiply both sides of the equation by $- \frac{2}{7}$ .

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

Simplify both sides of the equation.

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Simplify the left side.

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Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{2}{7}$ into the numerator.

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

Move the leading negative in $- \frac{7 n}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

$\frac{2 \cdot - 1}{7} \cdot \frac{- 7 n}{2} = - \frac{2}{7} \cdot 14$

Rewrite the expression.

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

Cancel the common factor of $7$ .

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Factor $7$ out of $- 7 n$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

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Multiply $- 1$ by $- 1$ .

$1 \cdot n = - \frac{2}{7} \cdot 14$

Multiply $n$ by $1$ .

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

Simplify $- \frac{2}{7} \cdot 14$ .

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Cancel the common factor of $7$ .

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Move the leading negative in $- \frac{2}{7}$ into the numerator.

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

Factor $7$ out of $14$ .

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

Cancel the common factor.

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

Rewrite the expression.

$n = - 2 \cdot 2$

Multiply $- 2$ by $2$ .

$n = - 4$

Solve for n 2-1/2n=3n+16

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