Algebra Examples

$11 a = \frac{b}{2} - 2 c (b + 7)$

Step 1

Divide each term in $11 a = \frac{b}{2} - 2 c (b + 7)$ by $11$ .

$\frac{11 a}{11} = \frac{\frac{b}{2}}{11} + \frac{- 2 c (b + 7)}{11}$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 2.1.1

Cancel the common factor.

$\frac{11 a}{11} = \frac{\frac{b}{2}}{11} + \frac{- 2 c (b + 7)}{11}$

Step 2.1.2

Divide $a$ by $1$ .

$a = \frac{\frac{b}{2}}{11} + \frac{- 2 c (b + 7)}{11}$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply the numerator by the reciprocal of the denominator.

$a = \frac{b}{2} \cdot \frac{1}{11} + \frac{- 2 c (b + 7)}{11}$

Step 3.1.2

Multiply $\frac{b}{2} \cdot \frac{1}{11}$ .

Tap for more steps...

Step 3.1.2.1

Multiply $\frac{b}{2}$ by $\frac{1}{11}$ .

$a = \frac{b}{2 \cdot 11} + \frac{- 2 c (b + 7)}{11}$

Step 3.1.2.2

Multiply $2$ by $11$ .

$a = \frac{b}{22} + \frac{- 2 c (b + 7)}{11}$

Step 3.1.3

Move the negative in front of the fraction.

$a = \frac{b}{22} - \frac{2 c (b + 7)}{11}$

Step 3.2

To write $- \frac{2 c (b + 7)}{11}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a = \frac{b}{22} - \frac{2 c (b + 7)}{11} \cdot \frac{2}{2}$

Step 3.3

Write each expression with a common denominator of $22$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{2 c (b + 7)}{11}$ by $\frac{2}{2}$ .

$a = \frac{b}{22} - \frac{2 c (b + 7) \cdot 2}{11 \cdot 2}$

Step 3.3.2

Multiply $11$ by $2$ .

$a = \frac{b}{22} - \frac{2 c (b + 7) \cdot 2}{22}$

Step 3.4

Combine the numerators over the common denominator.

$a = \frac{b - 2 c (b + 7) \cdot 2}{22}$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Apply the distributive property.

$a = \frac{b + (- 2 c b - 2 c \cdot 7) \cdot 2}{22}$

Step 3.5.2

Multiply $7$ by $- 2$ .

$a = \frac{b + (- 2 c b - 14 c) \cdot 2}{22}$

Step 3.5.3

Apply the distributive property.

$a = \frac{b - 2 c b \cdot 2 - 14 c \cdot 2}{22}$

Step 3.5.4

Multiply $2$ by $- 2$ .

$a = \frac{b - 4 c b - 14 c \cdot 2}{22}$

Step 3.5.5

Multiply $2$ by $- 14$ .

$a = \frac{b - 4 c b - 28 c}{22}$