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

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

Step 1

Rewrite the equation as $\frac{3}{8} + \frac{1}{2} b = \frac{1}{2}$ .

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

Step 2

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

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

Step 3

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

Subtract $\frac{3}{8}$ from both sides of the equation.

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

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

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

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

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

Multiply $2$ by $4$ .

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

Combine the numerators over the common denominator.

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

Subtract $3$ from $4$ .

$\frac{b}{2} = \frac{1}{8}$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{b}{2} = 2 (\frac{1}{8})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{b}{2} = 2 (\frac{1}{8})$

Rewrite the expression.

$b = 2 (\frac{1}{8})$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$b = 2 \frac{1}{2 (4)}$

Cancel the common factor.

$b = 2 \frac{1}{2 \cdot 4}$

Rewrite the expression.

$b = \frac{1}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = \frac{1}{4}$

Decimal Form:

$b = 0.25$

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

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