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

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

Step 1

Combine $c$ and $\frac{1}{5}$ .

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

Step 2

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

Add $\frac{5}{6}$ to both sides of the equation.

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

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Add $- 3$ and $5$ .

$- \frac{c}{5} = \frac{2}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$- \frac{c}{5} = \frac{2 (1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- \frac{c}{5} = \frac{1}{3}$

Step 3

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{c}{5}) = - 5 (\frac{1}{3})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $5$ .

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

$- 5 \frac{- c}{5} = - 5 (\frac{1}{3})$

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- c}{5} = - 5 (\frac{1}{3})$

Cancel the common factor.

$5 \cdot - 1 \frac{- c}{5} = - 5 (\frac{1}{3})$

Rewrite the expression.

$- - c = - 5 (\frac{1}{3})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 c = - 5 (\frac{1}{3})$

Multiply $c$ by $1$ .

$c = - 5 (\frac{1}{3})$

Simplify the right side.

Simplify $- 5 (\frac{1}{3})$ .

Combine $- 5$ and $\frac{1}{3}$ .

$c = \frac{- 5}{3}$

Move the negative in front of the fraction.

$c = - \frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{5}{3}$

Decimal Form:

$c = - 1.\overline{6}$

Mixed Number Form:

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

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

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