Solve for b 1/2b+4=1/8b+88

$\frac{1}{2} b + 4 = \frac{1}{8} b + 88$

Step 1

Combine $\frac{1}{2}$ and $b$ .

$\frac{b}{2} + 4 = \frac{1}{8} b + 88$

Step 2

Combine $\frac{1}{8}$ and $b$ .

$\frac{b}{2} + 4 = \frac{b}{8} + 88$

Step 3

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

Subtract $\frac{b}{8}$ from both sides of the equation.

$\frac{b}{2} + 4 - \frac{b}{8} = 88$

To write $\frac{b}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{b}{2} \cdot \frac{4}{4} - \frac{b}{8} + 4 = 88$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{b}{2}$ by $\frac{4}{4}$ .

$\frac{b \cdot 4}{2 \cdot 4} - \frac{b}{8} + 4 = 88$

Multiply $2$ by $4$ .

$\frac{b \cdot 4}{8} - \frac{b}{8} + 4 = 88$

Combine the numerators over the common denominator.

$\frac{b \cdot 4 - b}{8} + 4 = 88$

Subtract $b$ from $b \cdot 4$ .

Reorder $b$ and $4$ .

$\frac{4 \cdot b - b}{8} + 4 = 88$

Subtract $b$ from $4 \cdot b$ .

$\frac{3 \cdot b}{8} + 4 = 88$

$\frac{3 b}{8} + 4 = 88$

Step 4

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

Subtract $4$ from both sides of the equation.

$\frac{3 b}{8} = 88 - 4$

Subtract $4$ from $88$ .

$\frac{3 b}{8} = 84$

Step 5

Multiply both sides of the equation by $\frac{8}{3}$ .

$\frac{8}{3} \cdot \frac{3 b}{8} = \frac{8}{3} \cdot 84$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{8}{3} \cdot \frac{3 b}{8}$ .

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8}{3} \cdot \frac{3 b}{8} = \frac{8}{3} \cdot 84$

Rewrite the expression.

$\frac{1}{3} (3 b) = \frac{8}{3} \cdot 84$

Cancel the common factor of $3$ .

Factor $3$ out of $3 b$ .

$\frac{1}{3} (3 (b)) = \frac{8}{3} \cdot 84$

Cancel the common factor.

$\frac{1}{3} (3 b) = \frac{8}{3} \cdot 84$

Rewrite the expression.

$b = \frac{8}{3} \cdot 84$

Simplify the right side.

Simplify $\frac{8}{3} \cdot 84$ .

Cancel the common factor of $3$ .

Factor $3$ out of $84$ .

$b = \frac{8}{3} \cdot (3 (28))$

Cancel the common factor.

$b = \frac{8}{3} \cdot (3 \cdot 28)$

Rewrite the expression.

$b = 8 \cdot 28$

Multiply $8$ by $28$ .

$b = 224$

Solve for b 1/2b+4=1/8b+88

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