Solve for c 1/2=-3/8-5/6c

$\frac{1}{2} = - \frac{3}{8} - \frac{5}{6} c$

Rewrite the equation as $- \frac{3}{8} - \frac{5}{6} c = \frac{1}{2}$ .

$- \frac{3}{8} - \frac{5}{6} c = \frac{1}{2}$

Simplify each term.

Combine $c$ and $\frac{5}{6}$ .

$- \frac{3}{8} - \frac{c \cdot 5}{6} = \frac{1}{2}$

Move $5$ to the left of $c$ .

$- \frac{3}{8} - \frac{5 c}{6} = \frac{1}{2}$

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

Add $\frac{3}{8}$ to both sides of the equation.

$- \frac{5 c}{6} = \frac{1}{2} + \frac{3}{8}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{5 c}{6} = \frac{1}{2} \cdot \frac{4}{4} + \frac{3}{8}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$- \frac{5 c}{6} = \frac{4}{2 \cdot 4} + \frac{3}{8}$

Multiply $2$ by $4$ .

$- \frac{5 c}{6} = \frac{4}{8} + \frac{3}{8}$

Combine the numerators over the common denominator.

$- \frac{5 c}{6} = \frac{4 + 3}{8}$

Add $4$ and $3$ .

$- \frac{5 c}{6} = \frac{7}{8}$

Multiply both sides of the equation by $- \frac{6}{5}$ .

$- \frac{6}{5} (- \frac{5 c}{6}) = - \frac{6}{5} \cdot \frac{7}{8}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{5} (- \frac{5 c}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{- 6}{5} (- \frac{5 c}{6}) = - \frac{6}{5} \cdot \frac{7}{8}$

Move the leading negative in $- \frac{5 c}{6}$ into the numerator.

$\frac{- 6}{5} \cdot \frac{- 5 c}{6} = - \frac{6}{5} \cdot \frac{7}{8}$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{5} \cdot \frac{- 5 c}{6} = - \frac{6}{5} \cdot \frac{7}{8}$

Cancel the common factor.

$\frac{6 \cdot - 1}{5} \cdot \frac{- 5 c}{6} = - \frac{6}{5} \cdot \frac{7}{8}$

Rewrite the expression.

$\frac{- 1}{5} (- 5 c) = - \frac{6}{5} \cdot \frac{7}{8}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 c$ .

$\frac{- 1}{5} (5 (- c)) = - \frac{6}{5} \cdot \frac{7}{8}$

Cancel the common factor.

$\frac{- 1}{5} (5 (- c)) = - \frac{6}{5} \cdot \frac{7}{8}$

Rewrite the expression.

$- - c = - \frac{6}{5} \cdot \frac{7}{8}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 c = - \frac{6}{5} \cdot \frac{7}{8}$

Multiply $c$ by $1$ .

$c = - \frac{6}{5} \cdot \frac{7}{8}$

Simplify the right side.

Simplify $- \frac{6}{5} \cdot \frac{7}{8}$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$c = \frac{- 6}{5} \cdot \frac{7}{8}$

Factor $2$ out of $- 6$ .

$c = \frac{2 (- 3)}{5} \cdot \frac{7}{8}$

Factor $2$ out of $8$ .

$c = \frac{2 \cdot - 3}{5} \cdot \frac{7}{2 \cdot 4}$

Cancel the common factor.

$c = \frac{2 \cdot - 3}{5} \cdot \frac{7}{2 \cdot 4}$

Rewrite the expression.

$c = \frac{- 3}{5} \cdot \frac{7}{4}$

Multiply $\frac{- 3}{5}$ by $\frac{7}{4}$ .

$c = \frac{- 3 \cdot 7}{5 \cdot 4}$

Simplify the expression.

Multiply $- 3$ by $7$ .

$c = \frac{- 21}{5 \cdot 4}$

Multiply $5$ by $4$ .

$c = \frac{- 21}{20}$

Move the negative in front of the fraction.

$c = - \frac{21}{20}$

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{21}{20}$

Decimal Form:

$c = - 1.05$

Mixed Number Form:

$c = - 1 \frac{1}{20}$

Solve for c 1/2=-3/8-5/6c

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