Solve for c (2c)/3-(4c)/5=7

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

Step 1

Simplify $\frac{2 c}{3} - \frac{4 c}{5}$ .

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

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

To write $- \frac{4 c}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $5$ .

$\frac{2 c \cdot 5}{15} - \frac{4 c}{5} \cdot \frac{3}{3} = 7$

Multiply $\frac{4 c}{5}$ by $\frac{3}{3}$ .

$\frac{2 c \cdot 5}{15} - \frac{4 c \cdot 3}{5 \cdot 3} = 7$

Multiply $5$ by $3$ .

$\frac{2 c \cdot 5}{15} - \frac{4 c \cdot 3}{15} = 7$

Combine the numerators over the common denominator.

$\frac{2 c \cdot 5 - 4 c \cdot 3}{15} = 7$

Simplify the numerator.

Factor $2 c$ out of $2 c \cdot 5 - 4 c \cdot 3$ .

Factor $2 c$ out of $2 c \cdot 5$ .

$\frac{2 c (5) - 4 c \cdot 3}{15} = 7$

Factor $2 c$ out of $- 4 c \cdot 3$ .

$\frac{2 c (5) + 2 c (- 2 \cdot 3)}{15} = 7$

Factor $2 c$ out of $2 c (5) + 2 c (- 2 \cdot 3)$ .

$\frac{2 c (5 - 2 \cdot 3)}{15} = 7$

Multiply $- 2$ by $3$ .

$\frac{2 c (5 - 6)}{15} = 7$

Subtract $6$ from $5$ .

$\frac{2 c \cdot - 1}{15} = 7$

Multiply $- 1$ by $2$ .

$\frac{- 2 c}{15} = 7$

Move the negative in front of the fraction.

$- \frac{2 c}{15} = 7$

Step 2

Multiply both sides of the equation by $- \frac{15}{2}$ .

$- \frac{15}{2} (- \frac{2 c}{15}) = - \frac{15}{2} \cdot 7$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{15}{2} (- \frac{2 c}{15})$ .

Cancel the common factor of $15$ .

Move the leading negative in $- \frac{15}{2}$ into the numerator.

$\frac{- 15}{2} (- \frac{2 c}{15}) = - \frac{15}{2} \cdot 7$

Move the leading negative in $- \frac{2 c}{15}$ into the numerator.

$\frac{- 15}{2} \cdot \frac{- 2 c}{15} = - \frac{15}{2} \cdot 7$

Factor $15$ out of $- 15$ .

$\frac{15 (- 1)}{2} \cdot \frac{- 2 c}{15} = - \frac{15}{2} \cdot 7$

Cancel the common factor.

$\frac{15 \cdot - 1}{2} \cdot \frac{- 2 c}{15} = - \frac{15}{2} \cdot 7$

Rewrite the expression.

$\frac{- 1}{2} (- 2 c) = - \frac{15}{2} \cdot 7$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 c$ .

$\frac{- 1}{2} (2 (- c)) = - \frac{15}{2} \cdot 7$

Cancel the common factor.

$\frac{- 1}{2} (2 (- c)) = - \frac{15}{2} \cdot 7$

Rewrite the expression.

$- - c = - \frac{15}{2} \cdot 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 c = - \frac{15}{2} \cdot 7$

Multiply $c$ by $1$ .

$c = - \frac{15}{2} \cdot 7$

Simplify the right side.

Simplify $- \frac{15}{2} \cdot 7$ .

Multiply $- \frac{15}{2} \cdot 7$ .

Multiply $7$ by $- 1$ .

$c = - 7 (\frac{15}{2})$

Combine $- 7$ and $\frac{15}{2}$ .

$c = \frac{- 7 \cdot 15}{2}$

Multiply $- 7$ by $15$ .

$c = \frac{- 105}{2}$

Move the negative in front of the fraction.

$c = - \frac{105}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{105}{2}$

Decimal Form:

$c = - 52.5$

Mixed Number Form:

$c = - 52 \frac{1}{2}$

Solve for c (2c)/3-(4c)/5=7

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