Solve for n n/7-12=5n+5

$\frac{n}{7} - 12 = 5 n + 5$

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

Subtract $5 n$ from both sides of the equation.

$\frac{n}{7} - 12 - 5 n = 5$

To write $- 5 n$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{n}{7} - 5 n \cdot \frac{7}{7} - 12 = 5$

Combine $- 5 n$ and $\frac{7}{7}$ .

$\frac{n}{7} + \frac{- 5 n \cdot 7}{7} - 12 = 5$

Combine the numerators over the common denominator.

$\frac{n - 5 n \cdot 7}{7} - 12 = 5$

Simplify each term.

Simplify the numerator.

Factor $n$ out of $n - 5 n \cdot 7$ .

Raise $n$ to the power of $1$ .

$\frac{n^{1} - 5 n \cdot 7}{7} - 12 = 5$

Factor $n$ out of $n^{1}$ .

$\frac{n \cdot 1 - 5 n \cdot 7}{7} - 12 = 5$

Factor $n$ out of $- 5 n \cdot 7$ .

$\frac{n \cdot 1 + n (- 5 \cdot 7)}{7} - 12 = 5$

Factor $n$ out of $n \cdot 1 + n (- 5 \cdot 7)$ .

$\frac{n (1 - 5 \cdot 7)}{7} - 12 = 5$

Multiply $- 5$ by $7$ .

$\frac{n (1 - 35)}{7} - 12 = 5$

Subtract $35$ from $1$ .

$\frac{n \cdot - 34}{7} - 12 = 5$

Move $- 34$ to the left of $n$ .

$\frac{- 34 \cdot n}{7} - 12 = 5$

Move the negative in front of the fraction.

$- \frac{34 n}{7} - 12 = 5$

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

Add $12$ to both sides of the equation.

$- \frac{34 n}{7} = 5 + 12$

Add $5$ and $12$ .

$- \frac{34 n}{7} = 17$

Multiply both sides of the equation by $- \frac{7}{34}$ .

$- \frac{7}{34} (- \frac{34 n}{7}) = - \frac{7}{34} \cdot 17$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{7}{34} (- \frac{34 n}{7})$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{34}$ into the numerator.

$\frac{- 7}{34} (- \frac{34 n}{7}) = - \frac{7}{34} \cdot 17$

Move the leading negative in $- \frac{34 n}{7}$ into the numerator.

$\frac{- 7}{34} \cdot \frac{- 34 n}{7} = - \frac{7}{34} \cdot 17$

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{34} \cdot \frac{- 34 n}{7} = - \frac{7}{34} \cdot 17$

Cancel the common factor.

$\frac{7 \cdot - 1}{34} \cdot \frac{- 34 n}{7} = - \frac{7}{34} \cdot 17$

Rewrite the expression.

$\frac{- 1}{34} (- 34 n) = - \frac{7}{34} \cdot 17$

Cancel the common factor of $34$ .

Factor $34$ out of $- 34 n$ .

$\frac{- 1}{34} (34 (- n)) = - \frac{7}{34} \cdot 17$

Cancel the common factor.

$\frac{- 1}{34} (34 (- n)) = - \frac{7}{34} \cdot 17$

Rewrite the expression.

$- - n = - \frac{7}{34} \cdot 17$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 n = - \frac{7}{34} \cdot 17$

Multiply $n$ by $1$ .

$n = - \frac{7}{34} \cdot 17$

Simplify the right side.

Simplify $- \frac{7}{34} \cdot 17$ .

Cancel the common factor of $17$ .

Move the leading negative in $- \frac{7}{34}$ into the numerator.

$n = \frac{- 7}{34} \cdot 17$

Factor $17$ out of $34$ .

$n = \frac{- 7}{17 (2)} \cdot 17$

Cancel the common factor.

$n = \frac{- 7}{17 \cdot 2} \cdot 17$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$n = - 3.5$

Mixed Number Form:

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

Solve for n n/7-12=5n+5

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