Solve for n -11-2 1/4n=-7/8

$- 11 - 2 \frac{1}{4} n = - \frac{7}{8}$

Step 1

Simplify the left side.

Simplify $- 11 - 2 \frac{1}{4} n$ .

Convert $2 \frac{1}{4}$ to an improper fraction.

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

$- 11 - (2 + \frac{1}{4}) n = - \frac{7}{8}$

Add $2$ and $\frac{1}{4}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 11 - (2 \cdot \frac{4}{4} + \frac{1}{4}) n = - \frac{7}{8}$

Combine $2$ and $\frac{4}{4}$ .

$- 11 - (\frac{2 \cdot 4}{4} + \frac{1}{4}) n = - \frac{7}{8}$

Combine the numerators over the common denominator.

$- 11 - \frac{2 \cdot 4 + 1}{4} n = - \frac{7}{8}$

Simplify the numerator.

Multiply $2$ by $4$ .

$- 11 - \frac{8 + 1}{4} n = - \frac{7}{8}$

Add $8$ and $1$ .

$- 11 - \frac{9}{4} n = - \frac{7}{8}$

Simplify each term.

Combine $n$ and $\frac{9}{4}$ .

$- 11 - \frac{n \cdot 9}{4} = - \frac{7}{8}$

Move $9$ to the left of $n$ .

$- 11 - \frac{9 n}{4} = - \frac{7}{8}$

Step 2

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

Add $11$ to both sides of the equation.

$- \frac{9 n}{4} = - \frac{7}{8} + 11$

To write $11$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{9 n}{4} = - \frac{7}{8} + 11 \cdot \frac{8}{8}$

Combine $11$ and $\frac{8}{8}$ .

$- \frac{9 n}{4} = - \frac{7}{8} + \frac{11 \cdot 8}{8}$

Combine the numerators over the common denominator.

$- \frac{9 n}{4} = \frac{- 7 + 11 \cdot 8}{8}$

Simplify the numerator.

Multiply $11$ by $8$ .

$- \frac{9 n}{4} = \frac{- 7 + 88}{8}$

Add $- 7$ and $88$ .

$- \frac{9 n}{4} = \frac{81}{8}$

Step 3

Multiply both sides of the equation by $- \frac{4}{9}$ .

$- \frac{4}{9} (- \frac{9 n}{4}) = - \frac{4}{9} \cdot \frac{81}{8}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{9} (- \frac{9 n}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{9}$ into the numerator.

$\frac{- 4}{9} (- \frac{9 n}{4}) = - \frac{4}{9} \cdot \frac{81}{8}$

Move the leading negative in $- \frac{9 n}{4}$ into the numerator.

$\frac{- 4}{9} \cdot \frac{- 9 n}{4} = - \frac{4}{9} \cdot \frac{81}{8}$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{9} \cdot \frac{- 9 n}{4} = - \frac{4}{9} \cdot \frac{81}{8}$

Cancel the common factor.

$\frac{4 \cdot - 1}{9} \cdot \frac{- 9 n}{4} = - \frac{4}{9} \cdot \frac{81}{8}$

Rewrite the expression.

$\frac{- 1}{9} (- 9 n) = - \frac{4}{9} \cdot \frac{81}{8}$

Cancel the common factor of $9$ .

Factor $9$ out of $- 9 n$ .

$\frac{- 1}{9} (9 (- n)) = - \frac{4}{9} \cdot \frac{81}{8}$

Cancel the common factor.

$\frac{- 1}{9} (9 (- n)) = - \frac{4}{9} \cdot \frac{81}{8}$

Rewrite the expression.

$- - n = - \frac{4}{9} \cdot \frac{81}{8}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 n = - \frac{4}{9} \cdot \frac{81}{8}$

Multiply $n$ by $1$ .

$n = - \frac{4}{9} \cdot \frac{81}{8}$

Simplify the right side.

Simplify $- \frac{4}{9} \cdot \frac{81}{8}$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{9}$ into the numerator.

$n = \frac{- 4}{9} \cdot \frac{81}{8}$

Factor $4$ out of $- 4$ .

$n = \frac{4 (- 1)}{9} \cdot \frac{81}{8}$

Factor $4$ out of $8$ .

$n = \frac{4 \cdot - 1}{9} \cdot \frac{81}{4 \cdot 2}$

Cancel the common factor.

$n = \frac{4 \cdot - 1}{9} \cdot \frac{81}{4 \cdot 2}$

Rewrite the expression.

$n = \frac{- 1}{9} \cdot \frac{81}{2}$

Cancel the common factor of $9$ .

Factor $9$ out of $81$ .

$n = \frac{- 1}{9} \cdot \frac{9 (9)}{2}$

Cancel the common factor.

$n = \frac{- 1}{9} \cdot \frac{9 \cdot 9}{2}$

Rewrite the expression.

$n = - \frac{9}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{9}{2}$

Decimal Form:

$n = - 4.5$

Mixed Number Form:

$n = - 4 \frac{1}{2}$

Solve for n -11-2 1/4n=-7/8

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