Solve for b 3/8-3/10b=1/2

$\frac{3}{8} - \frac{3}{10} b = \frac{1}{2}$

Simplify each term.

Combine $b$ and $\frac{3}{10}$ .

$\frac{3}{8} - \frac{b \cdot 3}{10} = \frac{1}{2}$

Move $3$ to the left of $b$ .

$\frac{3}{8} - \frac{3 b}{10} = \frac{1}{2}$

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

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

$- \frac{3 b}{10} = \frac{1}{2} - \frac{3}{8}$

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

$- \frac{3 b}{10} = \frac{1}{2} \cdot \frac{4}{4} - \frac{3}{8}$

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

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

$- \frac{3 b}{10} = \frac{4}{2 \cdot 4} - \frac{3}{8}$

Multiply $2$ by $4$ .

$- \frac{3 b}{10} = \frac{4}{8} - \frac{3}{8}$

Combine the numerators over the common denominator.

$- \frac{3 b}{10} = \frac{4 - 3}{8}$

Subtract $3$ from $4$ .

$- \frac{3 b}{10} = \frac{1}{8}$

Multiply both sides of the equation by $- \frac{10}{3}$ .

$- \frac{10}{3} (- \frac{3 b}{10}) = - \frac{10}{3} \cdot \frac{1}{8}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{10}{3} (- \frac{3 b}{10})$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{10}{3}$ into the numerator.

$\frac{- 10}{3} (- \frac{3 b}{10}) = - \frac{10}{3} \cdot \frac{1}{8}$

Move the leading negative in $- \frac{3 b}{10}$ into the numerator.

$\frac{- 10}{3} \cdot \frac{- 3 b}{10} = - \frac{10}{3} \cdot \frac{1}{8}$

Factor $10$ out of $- 10$ .

$\frac{10 (- 1)}{3} \cdot \frac{- 3 b}{10} = - \frac{10}{3} \cdot \frac{1}{8}$

Cancel the common factor.

$\frac{10 \cdot - 1}{3} \cdot \frac{- 3 b}{10} = - \frac{10}{3} \cdot \frac{1}{8}$

Rewrite the expression.

$\frac{- 1}{3} (- 3 b) = - \frac{10}{3} \cdot \frac{1}{8}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 b$ .

$\frac{- 1}{3} (3 (- b)) = - \frac{10}{3} \cdot \frac{1}{8}$

Cancel the common factor.

$\frac{- 1}{3} (3 (- b)) = - \frac{10}{3} \cdot \frac{1}{8}$

Rewrite the expression.

$- - b = - \frac{10}{3} \cdot \frac{1}{8}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 b = - \frac{10}{3} \cdot \frac{1}{8}$

Multiply $b$ by $1$ .

$b = - \frac{10}{3} \cdot \frac{1}{8}$

Simplify the right side.

Simplify $- \frac{10}{3} \cdot \frac{1}{8}$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{10}{3}$ into the numerator.

$b = \frac{- 10}{3} \cdot \frac{1}{8}$

Factor $2$ out of $- 10$ .

$b = \frac{2 (- 5)}{3} \cdot \frac{1}{8}$

Factor $2$ out of $8$ .

$b = \frac{2 \cdot - 5}{3} \cdot \frac{1}{2 \cdot 4}$

Cancel the common factor.

$b = \frac{2 \cdot - 5}{3} \cdot \frac{1}{2 \cdot 4}$

Rewrite the expression.

$b = \frac{- 5}{3} \cdot \frac{1}{4}$

Multiply $\frac{- 5}{3}$ by $\frac{1}{4}$ .

$b = \frac{- 5}{3 \cdot 4}$

Simplify the expression.

Multiply $3$ by $4$ .

$b = \frac{- 5}{12}$

Move the negative in front of the fraction.

$b = - \frac{5}{12}$

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{5}{12}$

Decimal Form:

$b = - 0.41\overline{6}$

Solve for b 3/8-3/10b=1/2

Related Questions

Support LCMGCF.com by disabling your adblocker.