Algebra Examples

$10 = \frac{c}{3} - 4 + \frac{c}{6}$

Step 1

Rewrite the equation as $\frac{c}{3} - 4 + \frac{c}{6} = 10$ .

$\frac{c}{3} - 4 + \frac{c}{6} = 10$

Step 2

Simplify $\frac{c}{3} - 4 + \frac{c}{6}$ .

Tap for more steps...

Step 2.1

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

$\frac{c}{3} \cdot \frac{2}{2} + \frac{c}{6} - 4 = 10$

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

$\frac{c \cdot 2}{3 \cdot 2} + \frac{c}{6} - 4 = 10$

Step 2.2.2

Multiply $3$ by $2$ .

$\frac{c \cdot 2}{6} + \frac{c}{6} - 4 = 10$

Step 2.3

Combine the numerators over the common denominator.

$\frac{c \cdot 2 + c}{6} - 4 = 10$

Step 2.4

Add $c \cdot 2$ and $c$ .

Tap for more steps...

Step 2.4.1

Reorder $c$ and $2$ .

$\frac{2 \cdot c + c}{6} - 4 = 10$

Step 2.4.2

Add $2 \cdot c$ and $c$ .

$\frac{3 \cdot c}{6} - 4 = 10$

Step 2.5

Cancel the common factor of $3$ and $6$ .

Tap for more steps...

Step 2.5.1

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

$\frac{3 (c)}{6} - 4 = 10$

Step 2.5.2

Cancel the common factors.

Tap for more steps...

Step 2.5.2.1

Factor $3$ out of $6$ .

$\frac{3 c}{3 \cdot 2} - 4 = 10$

Step 2.5.2.2

Cancel the common factor.

$\frac{3 c}{3 \cdot 2} - 4 = 10$

Step 2.5.2.3

Rewrite the expression.

$\frac{c}{2} - 4 = 10$

Step 3

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

Tap for more steps...

Step 3.1

Add $4$ to both sides of the equation.

$\frac{c}{2} = 10 + 4$

Step 3.2

Add $10$ and $4$ .

$\frac{c}{2} = 14$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{c}{2} = 2 \cdot 14$

Step 5

Simplify both sides of the equation.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor.

$2 \frac{c}{2} = 2 \cdot 14$

Step 5.1.1.2

Rewrite the expression.

$c = 2 \cdot 14$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Multiply $2$ by $14$ .

$c = 28$