Solve for b 4=8b+10c

$4 = 8 b + 10 c$

Step 1

Rewrite the equation as $8 b + 10 c = 4$ .

$8 b + 10 c = 4$

Step 2

Subtract $10 c$ from both sides of the equation.

$8 b = 4 - 10 c$

Step 3

Divide each term in $8 b = 4 - 10 c$ by $8$ and simplify.

Divide each term in $8 b = 4 - 10 c$ by $8$ .

$\frac{8 b}{8} = \frac{4}{8} + \frac{- 10 c}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 b}{8} = \frac{4}{8} + \frac{- 10 c}{8}$

Divide $b$ by $1$ .

$b = \frac{4}{8} + \frac{- 10 c}{8}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

$b = \frac{4 (1)}{8} + \frac{- 10 c}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$b = \frac{4 \cdot 1}{4 \cdot 2} + \frac{- 10 c}{8}$

Cancel the common factor.

$b = \frac{4 \cdot 1}{4 \cdot 2} + \frac{- 10 c}{8}$

Rewrite the expression.

$b = \frac{1}{2} + \frac{- 10 c}{8}$

Cancel the common factor of $- 10$ and $8$ .

Factor $2$ out of $- 10 c$ .

$b = \frac{1}{2} + \frac{2 (- 5 c)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$b = \frac{1}{2} + \frac{2 (- 5 c)}{2 (4)}$

Cancel the common factor.

$b = \frac{1}{2} + \frac{2 (- 5 c)}{2 \cdot 4}$

Rewrite the expression.

$b = \frac{1}{2} + \frac{- 5 c}{4}$

Move the negative in front of the fraction.

$b = \frac{1}{2} - \frac{5 c}{4}$