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

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

Step 1

Simplify $- 2 c + \frac{5}{6} - \frac{1}{3} c$ .

Combine $c$ and $\frac{1}{3}$ .

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

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

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

Simplify terms.

Combine $- 2 c$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $c$ out of $- 2 c \cdot 3 - c$ .

Factor $c$ out of $- 2 c \cdot 3$ .

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

Factor $c$ out of $- c$ .

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

Factor $c$ out of $c (- 2 \cdot 3) + c \cdot - 1$ .

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

Multiply $- 2$ by $3$ .

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

Subtract $1$ from $- 6$ .

$\frac{c \cdot - 7}{3} + \frac{5}{6} = \frac{3}{2} - \frac{5}{2} c + 2$

Move $- 7$ to the left of $c$ .

$\frac{- 7 \cdot c}{3} + \frac{5}{6} = \frac{3}{2} - \frac{5}{2} c + 2$

Move the negative in front of the fraction.

$- \frac{7 c}{3} + \frac{5}{6} = \frac{3}{2} - \frac{5}{2} c + 2$

Step 2

Simplify $\frac{3}{2} - \frac{5}{2} c + 2$ .

Simplify each term.

Combine $c$ and $\frac{5}{2}$ .

$- \frac{7 c}{3} + \frac{5}{6} = \frac{3}{2} - \frac{c \cdot 5}{2} + 2$

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

$- \frac{7 c}{3} + \frac{5}{6} = \frac{3}{2} - \frac{5 c}{2} + 2$

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

$- \frac{7 c}{3} + \frac{5}{6} = - \frac{5 c}{2} + \frac{3}{2} + 2 \cdot \frac{2}{2}$

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

$- \frac{7 c}{3} + \frac{5}{6} = - \frac{5 c}{2} + \frac{3}{2} + \frac{2 \cdot 2}{2}$

Combine the numerators over the common denominator.

$- \frac{7 c}{3} + \frac{5}{6} = - \frac{5 c}{2} + \frac{3 + 2 \cdot 2}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$- \frac{7 c}{3} + \frac{5}{6} = - \frac{5 c}{2} + \frac{3 + 4}{2}$

Add $3$ and $4$ .

$- \frac{7 c}{3} + \frac{5}{6} = - \frac{5 c}{2} + \frac{7}{2}$

Step 3

Move all terms containing $c$ to the left side of the equation.

Add $\frac{5 c}{2}$ to both sides of the equation.

$- \frac{7 c}{3} + \frac{5}{6} + \frac{5 c}{2} = \frac{7}{2}$

To write $- \frac{7 c}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{7 c}{3} \cdot \frac{2}{2} + \frac{5 c}{2} + \frac{5}{6} = \frac{7}{2}$

To write $\frac{5 c}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7 c}{3} \cdot \frac{2}{2} + \frac{5 c}{2} \cdot \frac{3}{3} + \frac{5}{6} = \frac{7}{2}$

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

Multiply $\frac{7 c}{3}$ by $\frac{2}{2}$ .

$- \frac{7 c \cdot 2}{3 \cdot 2} + \frac{5 c}{2} \cdot \frac{3}{3} + \frac{5}{6} = \frac{7}{2}$

Multiply $3$ by $2$ .

$- \frac{7 c \cdot 2}{6} + \frac{5 c}{2} \cdot \frac{3}{3} + \frac{5}{6} = \frac{7}{2}$

Multiply $\frac{5 c}{2}$ by $\frac{3}{3}$ .

$- \frac{7 c \cdot 2}{6} + \frac{5 c \cdot 3}{2 \cdot 3} + \frac{5}{6} = \frac{7}{2}$

Multiply $2$ by $3$ .

$- \frac{7 c \cdot 2}{6} + \frac{5 c \cdot 3}{6} + \frac{5}{6} = \frac{7}{2}$

Combine the numerators over the common denominator.

$\frac{- 7 c \cdot 2 + 5 c \cdot 3}{6} + \frac{5}{6} = \frac{7}{2}$

Combine the numerators over the common denominator.

$\frac{- 7 c \cdot 2 + 5 c \cdot 3 + 5}{6} = \frac{7}{2}$

Simplify each term.

Multiply $2$ by $- 7$ .

$\frac{- 14 c + 5 c \cdot 3 + 5}{6} = \frac{7}{2}$

Multiply $3$ by $5$ .

$\frac{- 14 c + 15 c + 5}{6} = \frac{7}{2}$

Add $- 14 c$ and $15 c$ .

$\frac{c + 5}{6} = \frac{7}{2}$

Step 4

Multiply both sides of the equation by $6$ .

$6 \frac{c + 5}{6} = 6 (\frac{7}{2})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{c + 5}{6} = 6 (\frac{7}{2})$

Rewrite the expression.

$c + 5 = 6 (\frac{7}{2})$

Simplify the right side.

Simplify $6 (\frac{7}{2})$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$c + 5 = 2 (3) \frac{7}{2}$

Cancel the common factor.

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

Rewrite the expression.

$c + 5 = 3 \cdot 7$

Multiply $3$ by $7$ .

$c + 5 = 21$

Step 6

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

Subtract $5$ from both sides of the equation.

$c = 21 - 5$

Subtract $5$ from $21$ .

$c = 16$

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

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