Solve for b 2/5b-1/2=-6/7

$\frac{2}{5} b - \frac{1}{2} = - \frac{6}{7}$

Step 1

Combine $\frac{2}{5}$ and $b$ .

$\frac{2 b}{5} - \frac{1}{2} = - \frac{6}{7}$

Step 2

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

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{2 b}{5} = - \frac{6}{7} + \frac{1}{2}$

To write $- \frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 b}{5} = - \frac{6}{7} \cdot \frac{2}{2} + \frac{1}{2}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2 b}{5} = - \frac{6}{7} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{7}{7}$

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6}{7}$ by $\frac{2}{2}$ .

$\frac{2 b}{5} = - \frac{6 \cdot 2}{7 \cdot 2} + \frac{1}{2} \cdot \frac{7}{7}$

Multiply $7$ by $2$ .

$\frac{2 b}{5} = - \frac{6 \cdot 2}{14} + \frac{1}{2} \cdot \frac{7}{7}$

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$\frac{2 b}{5} = - \frac{6 \cdot 2}{14} + \frac{7}{2 \cdot 7}$

Multiply $2$ by $7$ .

$\frac{2 b}{5} = - \frac{6 \cdot 2}{14} + \frac{7}{14}$

Combine the numerators over the common denominator.

$\frac{2 b}{5} = \frac{- 6 \cdot 2 + 7}{14}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$\frac{2 b}{5} = \frac{- 12 + 7}{14}$

Add $- 12$ and $7$ .

$\frac{2 b}{5} = \frac{- 5}{14}$

Move the negative in front of the fraction.

$\frac{2 b}{5} = - \frac{5}{14}$

Step 3

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 b}{5} = \frac{5}{2} (- \frac{5}{14})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{2} \cdot \frac{2 b}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 b}{5} = \frac{5}{2} (- \frac{5}{14})$

Rewrite the expression.

$\frac{1}{2} (2 b) = \frac{5}{2} (- \frac{5}{14})$

Cancel the common factor of $2$ .

Factor $2$ out of $2 b$ .

$\frac{1}{2} (2 (b)) = \frac{5}{2} (- \frac{5}{14})$

Cancel the common factor.

$\frac{1}{2} (2 b) = \frac{5}{2} (- \frac{5}{14})$

Rewrite the expression.

$b = \frac{5}{2} (- \frac{5}{14})$

Simplify the right side.

Multiply $\frac{5}{2} (- \frac{5}{14})$ .

Multiply $\frac{5}{2}$ by $\frac{5}{14}$ .

$b = - \frac{5 \cdot 5}{2 \cdot 14}$

Multiply $5$ by $5$ .

$b = - \frac{25}{2 \cdot 14}$

Multiply $2$ by $14$ .

$b = - \frac{25}{28}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{25}{28}$

Decimal Form:

$b = - 0.89285714 \dots$

Solve for b 2/5b-1/2=-6/7

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