Basic Math Examples

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

Step 1

Multiply both sides by $7$ .

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

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $(\frac{2 (c + 5)}{3} - 4) \cdot 7$ .

Tap for more steps...

Step 2.2.1.1

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

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

Step 2.2.1.2

Simplify terms.

Tap for more steps...

Step 2.2.1.2.1

Combine $- 4$ and $\frac{3}{3}$ .

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

Step 2.2.1.2.2

Combine the numerators over the common denominator.

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

Step 2.2.1.3

Simplify the numerator.

Tap for more steps...

Step 2.2.1.3.1

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

Tap for more steps...

Step 2.2.1.3.1.1

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

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

Step 2.2.1.3.1.2

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

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

Step 2.2.1.3.2

Multiply $- 2$ by $3$ .

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

Step 2.2.1.3.3

Subtract $6$ from $5$ .

$6 c = \frac{2 (c - 1)}{3} \cdot 7$

Step 2.2.1.4

Multiply $\frac{2 (c - 1)}{3} \cdot 7$ .

Tap for more steps...

Step 2.2.1.4.1

Combine $\frac{2 (c - 1)}{3}$ and $7$ .

$6 c = \frac{2 (c - 1) \cdot 7}{3}$

Step 2.2.1.4.2

Multiply $7$ by $2$ .

$6 c = \frac{14 (c - 1)}{3}$

Step 3

Solve for $c$ .

Tap for more steps...

Step 3.1

Multiply both sides by $3$ .

$6 c \cdot 3 = \frac{14 (c - 1)}{3} \cdot 3$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Multiply $3$ by $6$ .

$18 c = \frac{14 (c - 1)}{3} \cdot 3$

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Simplify $\frac{14 (c - 1)}{3} \cdot 3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.2.1.1.1

Cancel the common factor.

$18 c = \frac{14 (c - 1)}{3} \cdot 3$

Step 3.2.2.1.1.2

Rewrite the expression.

$18 c = 14 (c - 1)$

Step 3.2.2.1.2

Apply the distributive property.

$18 c = 14 c + 14 \cdot - 1$

Step 3.2.2.1.3

Multiply $14$ by $- 1$ .

$18 c = 14 c - 14$

Step 3.3

Solve for $c$ .

Tap for more steps...

Step 3.3.1

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

Tap for more steps...

Step 3.3.1.1

Subtract $14 c$ from both sides of the equation.

$18 c - 14 c = - 14$

Step 3.3.1.2

Subtract $14 c$ from $18 c$ .

$4 c = - 14$

Step 3.3.2

Divide each term in $4 c = - 14$ by $4$ and simplify.

Tap for more steps...

Step 3.3.2.1

Divide each term in $4 c = - 14$ by $4$ .

$\frac{4 c}{4} = \frac{- 14}{4}$

Step 3.3.2.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{4 c}{4} = \frac{- 14}{4}$

Step 3.3.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{- 14}{4}$

Step 3.3.2.3

Simplify the right side.

Tap for more steps...

Step 3.3.2.3.1

Cancel the common factor of $- 14$ and $4$ .

Tap for more steps...

Step 3.3.2.3.1.1

Factor $2$ out of $- 14$ .

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

Step 3.3.2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.3.1.2.1

Factor $2$ out of $4$ .

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

Step 3.3.2.3.1.2.2

Cancel the common factor.

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

Step 3.3.2.3.1.2.3

Rewrite the expression.

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

Step 3.3.2.3.2

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$c = - 3.5$

Mixed Number Form:

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