Solve for k -k-7/2k=57/4

$- k - \frac{7}{2} k = \frac{57}{4}$

Step 1

Simplify $- k - \frac{7}{2} k$ .

Simplify each term.

Combine $k$ and $\frac{7}{2}$ .

$- k - \frac{k \cdot 7}{2} = \frac{57}{4}$

Move $7$ to the left of $k$ .

$- k - \frac{7 k}{2} = \frac{57}{4}$

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

$- k \cdot \frac{2}{2} - \frac{7 k}{2} = \frac{57}{4}$

Simplify terms.

Combine $- k$ and $\frac{2}{2}$ .

$\frac{- k \cdot 2}{2} - \frac{7 k}{2} = \frac{57}{4}$

Combine the numerators over the common denominator.

$\frac{- k \cdot 2 - 7 k}{2} = \frac{57}{4}$

Simplify the numerator.

Factor $k$ out of $- k \cdot 2 - 7 k$ .

Factor $k$ out of $- k \cdot 2$ .

$\frac{k (- 1 \cdot 2) - 7 k}{2} = \frac{57}{4}$

Factor $k$ out of $- 7 k$ .

$\frac{k (- 1 \cdot 2) + k \cdot - 7}{2} = \frac{57}{4}$

Factor $k$ out of $k (- 1 \cdot 2) + k \cdot - 7$ .

$\frac{k (- 1 \cdot 2 - 7)}{2} = \frac{57}{4}$

Multiply $- 1$ by $2$ .

$\frac{k (- 2 - 7)}{2} = \frac{57}{4}$

Subtract $7$ from $- 2$ .

$\frac{k \cdot - 9}{2} = \frac{57}{4}$

Simplify the expression.

Move $- 9$ to the left of $k$ .

$\frac{- 9 \cdot k}{2} = \frac{57}{4}$

Move the negative in front of the fraction.

$- \frac{9 k}{2} = \frac{57}{4}$

Step 2

Multiply both sides of the equation by $- \frac{2}{9}$ .

$- \frac{2}{9} (- \frac{9 k}{2}) = - \frac{2}{9} \cdot \frac{57}{4}$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{9} (- \frac{9 k}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$\frac{- 2}{9} (- \frac{9 k}{2}) = - \frac{2}{9} \cdot \frac{57}{4}$

Move the leading negative in $- \frac{9 k}{2}$ into the numerator.

$\frac{- 2}{9} \cdot \frac{- 9 k}{2} = - \frac{2}{9} \cdot \frac{57}{4}$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{9} \cdot \frac{- 9 k}{2} = - \frac{2}{9} \cdot \frac{57}{4}$

Cancel the common factor.

$\frac{2 \cdot - 1}{9} \cdot \frac{- 9 k}{2} = - \frac{2}{9} \cdot \frac{57}{4}$

Rewrite the expression.

$\frac{- 1}{9} (- 9 k) = - \frac{2}{9} \cdot \frac{57}{4}$

Cancel the common factor of $9$ .

Factor $9$ out of $- 9 k$ .

$\frac{- 1}{9} (9 (- k)) = - \frac{2}{9} \cdot \frac{57}{4}$

Cancel the common factor.

$\frac{- 1}{9} (9 (- k)) = - \frac{2}{9} \cdot \frac{57}{4}$

Rewrite the expression.

$- - k = - \frac{2}{9} \cdot \frac{57}{4}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 k = - \frac{2}{9} \cdot \frac{57}{4}$

Multiply $k$ by $1$ .

$k = - \frac{2}{9} \cdot \frac{57}{4}$

Simplify the right side.

Simplify $- \frac{2}{9} \cdot \frac{57}{4}$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$k = \frac{- 2}{9} \cdot \frac{57}{4}$

Factor $2$ out of $- 2$ .

$k = \frac{2 (- 1)}{9} \cdot \frac{57}{4}$

Factor $2$ out of $4$ .

$k = \frac{2 \cdot - 1}{9} \cdot \frac{57}{2 \cdot 2}$

Cancel the common factor.

$k = \frac{2 \cdot - 1}{9} \cdot \frac{57}{2 \cdot 2}$

Rewrite the expression.

$k = \frac{- 1}{9} \cdot \frac{57}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

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

Factor $3$ out of $57$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{- 1}{3}$ by $\frac{19}{2}$ .

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

Simplify the expression.

Multiply $- 1$ by $19$ .

$k = \frac{- 19}{3 \cdot 2}$

Multiply $3$ by $2$ .

$k = \frac{- 19}{6}$

Move the negative in front of the fraction.

$k = - \frac{19}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{19}{6}$

Decimal Form:

$k = - 3.1\overline{6}$

Mixed Number Form:

$k = - 3 \frac{1}{6}$

Solve for k -k-7/2k=57/4

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