Solve for b 1/2(4a+10b)=c

$\frac{1}{2} (4 a + 10 b) = c$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (4 a + 10 b)) = 2 c$

Step 2

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (4 a + 10 b))$ .

Apply the distributive property.

$2 (\frac{1}{2} (4 a) + \frac{1}{2} (10 b)) = 2 c$

Cancel the common factor of $2$ .

Factor $2$ out of $4 a$ .

$2 (\frac{1}{2} (2 (2 a)) + \frac{1}{2} (10 b)) = 2 c$

Cancel the common factor.

$2 (\frac{1}{2} (2 (2 a)) + \frac{1}{2} (10 b)) = 2 c$

Rewrite the expression.

$2 (2 a + \frac{1}{2} (10 b)) = 2 c$

Cancel the common factor of $2$ .

Factor $2$ out of $10 b$ .

$2 (2 a + \frac{1}{2} (2 (5 b))) = 2 c$

Cancel the common factor.

$2 (2 a + \frac{1}{2} (2 (5 b))) = 2 c$

Rewrite the expression.

$2 (2 a + 5 b) = 2 c$

Apply the distributive property.

$2 (2 a) + 2 (5 b) = 2 c$

Multiply.

Multiply $2$ by $2$ .

$4 a + 2 (5 b) = 2 c$

Multiply $5$ by $2$ .

$4 a + 10 b = 2 c$

Step 3

Subtract $4 a$ from both sides of the equation.

$10 b = 2 c - 4 a$

Step 4

Divide each term in $10 b = 2 c - 4 a$ by $10$ and simplify.

Divide each term in $10 b = 2 c - 4 a$ by $10$ .

$\frac{10 b}{10} = \frac{2 c}{10} + \frac{- 4 a}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 b}{10} = \frac{2 c}{10} + \frac{- 4 a}{10}$

Divide $b$ by $1$ .

$b = \frac{2 c}{10} + \frac{- 4 a}{10}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2 c$ .

$b = \frac{2 (c)}{10} + \frac{- 4 a}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$b = \frac{2 c}{2 \cdot 5} + \frac{- 4 a}{10}$

Cancel the common factor.

$b = \frac{2 c}{2 \cdot 5} + \frac{- 4 a}{10}$

Rewrite the expression.

$b = \frac{c}{5} + \frac{- 4 a}{10}$

Cancel the common factor of $- 4$ and $10$ .

Factor $2$ out of $- 4 a$ .

$b = \frac{c}{5} + \frac{2 (- 2 a)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$b = \frac{c}{5} + \frac{2 (- 2 a)}{2 (5)}$

Cancel the common factor.

$b = \frac{c}{5} + \frac{2 (- 2 a)}{2 \cdot 5}$

Rewrite the expression.

$b = \frac{c}{5} + \frac{- 2 a}{5}$

Move the negative in front of the fraction.

$b = \frac{c}{5} - \frac{2 a}{5}$

Solve for b 1/2(4a+10b)=c

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