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

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

Step 1

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

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

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.

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

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

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

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

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

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

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

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

Multiply $7$ by $2$ .

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

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

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

Multiply $2$ by $7$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $6$ by $2$ .

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

Add $12$ and $7$ .

$- \frac{b}{2} = \frac{19}{14}$

Step 3

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{b}{2}) = - 2 (\frac{19}{14})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{b}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{b}{2}$ into the numerator.

$- 2 \frac{- b}{2} = - 2 (\frac{19}{14})$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- b}{2} = - 2 (\frac{19}{14})$

Cancel the common factor.

$2 \cdot - 1 \frac{- b}{2} = - 2 (\frac{19}{14})$

Rewrite the expression.

$- - b = - 2 (\frac{19}{14})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 b = - 2 (\frac{19}{14})$

Multiply $b$ by $1$ .

$b = - 2 (\frac{19}{14})$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$b = 2 (- 1) \frac{19}{14}$

Factor $2$ out of $14$ .

$b = 2 \cdot - 1 \frac{19}{2 \cdot 7}$

Cancel the common factor.

$b = 2 \cdot - 1 \frac{19}{2 \cdot 7}$

Rewrite the expression.

$b = - \frac{19}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{19}{7}$

Decimal Form:

$b = - 2.\overline{714285}$

Mixed Number Form:

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

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

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