Solve for n -8-5 1/4n=-7/8

$- 8 - 5 \frac{1}{4} n = - \frac{7}{8}$

Simplify the left side.

Simplify $- 8 - 5 \frac{1}{4} n$ .

Convert $5 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- 8 - (5 + \frac{1}{4}) n = - \frac{7}{8}$

Add $5$ and $\frac{1}{4}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 8 - (5 \cdot \frac{4}{4} + \frac{1}{4}) n = - \frac{7}{8}$

Combine $5$ and $\frac{4}{4}$ .

$- 8 - (\frac{5 \cdot 4}{4} + \frac{1}{4}) n = - \frac{7}{8}$

Combine the numerators over the common denominator.

$- 8 - \frac{5 \cdot 4 + 1}{4} n = - \frac{7}{8}$

Simplify the numerator.

Multiply $5$ by $4$ .

$- 8 - \frac{20 + 1}{4} n = - \frac{7}{8}$

Add $20$ and $1$ .

$- 8 - \frac{21}{4} n = - \frac{7}{8}$

Simplify each term.

Combine $n$ and $\frac{21}{4}$ .

$- 8 - \frac{n \cdot 21}{4} = - \frac{7}{8}$

Move $21$ to the left of $n$ .

$- 8 - \frac{21 n}{4} = - \frac{7}{8}$

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

Add $8$ to both sides of the equation.

$- \frac{21 n}{4} = - \frac{7}{8} + 8$

To write $8$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{21 n}{4} = - \frac{7}{8} + 8 \cdot \frac{8}{8}$

Combine $8$ and $\frac{8}{8}$ .

$- \frac{21 n}{4} = - \frac{7}{8} + \frac{8 \cdot 8}{8}$

Combine the numerators over the common denominator.

$- \frac{21 n}{4} = \frac{- 7 + 8 \cdot 8}{8}$

Simplify the numerator.

Multiply $8$ by $8$ .

$- \frac{21 n}{4} = \frac{- 7 + 64}{8}$

Add $- 7$ and $64$ .

$- \frac{21 n}{4} = \frac{57}{8}$

Multiply both sides of the equation by $- \frac{4}{21}$ .

$- \frac{4}{21} (- \frac{21 n}{4}) = - \frac{4}{21} \cdot \frac{57}{8}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{21} (- \frac{21 n}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{21}$ into the numerator.

$\frac{- 4}{21} (- \frac{21 n}{4}) = - \frac{4}{21} \cdot \frac{57}{8}$

Move the leading negative in $- \frac{21 n}{4}$ into the numerator.

$\frac{- 4}{21} \cdot \frac{- 21 n}{4} = - \frac{4}{21} \cdot \frac{57}{8}$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{21} \cdot \frac{- 21 n}{4} = - \frac{4}{21} \cdot \frac{57}{8}$

Cancel the common factor.

$\frac{4 \cdot - 1}{21} \cdot \frac{- 21 n}{4} = - \frac{4}{21} \cdot \frac{57}{8}$

Rewrite the expression.

$\frac{- 1}{21} (- 21 n) = - \frac{4}{21} \cdot \frac{57}{8}$

Cancel the common factor of $21$ .

Factor $21$ out of $- 21 n$ .

$\frac{- 1}{21} (21 (- n)) = - \frac{4}{21} \cdot \frac{57}{8}$

Cancel the common factor.

$\frac{- 1}{21} (21 (- n)) = - \frac{4}{21} \cdot \frac{57}{8}$

Rewrite the expression.

$- - n = - \frac{4}{21} \cdot \frac{57}{8}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 n = - \frac{4}{21} \cdot \frac{57}{8}$

Multiply $n$ by $1$ .

$n = - \frac{4}{21} \cdot \frac{57}{8}$

Simplify the right side.

Simplify $- \frac{4}{21} \cdot \frac{57}{8}$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{21}$ into the numerator.

$n = \frac{- 4}{21} \cdot \frac{57}{8}$

Factor $4$ out of $- 4$ .

$n = \frac{4 (- 1)}{21} \cdot \frac{57}{8}$

Factor $4$ out of $8$ .

$n = \frac{4 \cdot - 1}{21} \cdot \frac{57}{4 \cdot 2}$

Cancel the common factor.

$n = \frac{4 \cdot - 1}{21} \cdot \frac{57}{4 \cdot 2}$

Rewrite the expression.

$n = \frac{- 1}{21} \cdot \frac{57}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

$n = \frac{- 1}{3 (7)} \cdot \frac{57}{2}$

Factor $3$ out of $57$ .

$n = \frac{- 1}{3 \cdot 7} \cdot \frac{3 \cdot 19}{2}$

Cancel the common factor.

$n = \frac{- 1}{3 \cdot 7} \cdot \frac{3 \cdot 19}{2}$

Rewrite the expression.

$n = \frac{- 1}{7} \cdot \frac{19}{2}$

Multiply $\frac{- 1}{7}$ by $\frac{19}{2}$ .

$n = \frac{- 1 \cdot 19}{7 \cdot 2}$

Simplify the expression.

Multiply $- 1$ by $19$ .

$n = \frac{- 19}{7 \cdot 2}$

Multiply $7$ by $2$ .

$n = \frac{- 19}{14}$

Move the negative in front of the fraction.

$n = - \frac{19}{14}$

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{19}{14}$

Decimal Form:

$n = - 1.35714285 \dots$

Mixed Number Form:

$n = - 1 \frac{5}{14}$

Solve for n -8-5 1/4n=-7/8

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