Solve for b 3/8-1/8b=3/4b+1/2

$\frac{3}{8} - \frac{1}{8} b = \frac{3}{4} b + \frac{1}{2}$

Step 1

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

$\frac{3}{8} - \frac{b}{8} = \frac{3}{4} b + \frac{1}{2}$

Step 2

Combine $\frac{3}{4}$ and $b$ .

$\frac{3}{8} - \frac{b}{8} = \frac{3 b}{4} + \frac{1}{2}$

Step 3

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

Subtract $\frac{3 b}{4}$ from both sides of the equation.

$\frac{3}{8} - \frac{b}{8} - \frac{3 b}{4} = \frac{1}{2}$

To write $- \frac{3 b}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{8} - \frac{b}{8} - \frac{3 b}{4} \cdot \frac{2}{2} = \frac{1}{2}$

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

Multiply $\frac{3 b}{4}$ by $\frac{2}{2}$ .

$\frac{3}{8} - \frac{b}{8} - \frac{3 b \cdot 2}{4 \cdot 2} = \frac{1}{2}$

Multiply $4$ by $2$ .

$\frac{3}{8} - \frac{b}{8} - \frac{3 b \cdot 2}{8} = \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{3}{8} + \frac{- b - 3 b \cdot 2}{8} = \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{3 - b - 3 b \cdot 2}{8} = \frac{1}{2}$

Multiply $2$ by $- 3$ .

$\frac{3 - b - 6 b}{8} = \frac{1}{2}$

Subtract $6 b$ from $- b$ .

$\frac{3 - 7 b}{8} = \frac{1}{2}$

Step 4

Multiply both sides by $8$ .

$\frac{3 - 7 b}{8} \cdot 8 = \frac{1}{2} \cdot 8$

Step 5

Simplify.

Simplify the left side.

Simplify $\frac{3 - 7 b}{8} \cdot 8$ .

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{3 - 7 b}{8} \cdot 8 = \frac{1}{2} \cdot 8$

Rewrite the expression.

$3 - 7 b = \frac{1}{2} \cdot 8$

Reorder $3$ and $- 7 b$ .

$- 7 b + 3 = \frac{1}{2} \cdot 8$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$- 7 b + 3 = \frac{1}{2} \cdot (2 (4))$

Cancel the common factor.

$- 7 b + 3 = \frac{1}{2} \cdot (2 \cdot 4)$

Rewrite the expression.

$- 7 b + 3 = 4$

Step 6

Solve for $b$ .

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

Subtract $3$ from both sides of the equation.

$- 7 b = 4 - 3$

Subtract $3$ from $4$ .

$- 7 b = 1$

Divide each term in $- 7 b = 1$ by $- 7$ and simplify.

Divide each term in $- 7 b = 1$ by $- 7$ .

$\frac{- 7 b}{- 7} = \frac{1}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 b}{- 7} = \frac{1}{- 7}$

Divide $b$ by $1$ .

$b = \frac{1}{- 7}$

Simplify the right side.

Move the negative in front of the fraction.

$b = - \frac{1}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{1}{7}$

Decimal Form:

$b = - 0.\overline{142857}$

Solve for b 3/8-1/8b=3/4b+1/2

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