Solve for b (2b-3)/7-b/2=(b+3)/14

$\frac{2 b - 3}{7} - \frac{b}{2} = \frac{b + 3}{14}$

Multiply both sides by $14$ .

$(\frac{2 b - 3}{7} - \frac{b}{2}) \cdot 14 = \frac{b + 3}{14} \cdot 14$

Simplify.

Simplify the left side.

Simplify $(\frac{2 b - 3}{7} - \frac{b}{2}) \cdot 14$ .

To write $\frac{2 b - 3}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{2 b - 3}{7} \cdot \frac{2}{2} - \frac{b}{2}) \cdot 14 = \frac{b + 3}{14} \cdot 14$

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

$(\frac{2 b - 3}{7} \cdot \frac{2}{2} - \frac{b}{2} \cdot \frac{7}{7}) \cdot 14 = \frac{b + 3}{14} \cdot 14$

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

Multiply $\frac{2 b - 3}{7}$ by $\frac{2}{2}$ .

$(\frac{(2 b - 3) \cdot 2}{7 \cdot 2} - \frac{b}{2} \cdot \frac{7}{7}) \cdot 14 = \frac{b + 3}{14} \cdot 14$

Multiply $7$ by $2$ .

$(\frac{(2 b - 3) \cdot 2}{14} - \frac{b}{2} \cdot \frac{7}{7}) \cdot 14 = \frac{b + 3}{14} \cdot 14$

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

$(\frac{(2 b - 3) \cdot 2}{14} - \frac{b \cdot 7}{2 \cdot 7}) \cdot 14 = \frac{b + 3}{14} \cdot 14$

Multiply $2$ by $7$ .

$(\frac{(2 b - 3) \cdot 2}{14} - \frac{b \cdot 7}{14}) \cdot 14 = \frac{b + 3}{14} \cdot 14$

Combine the numerators over the common denominator.

$\frac{(2 b - 3) \cdot 2 - b \cdot 7}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Simplify the numerator.

Apply the distributive property.

$\frac{2 b \cdot 2 - 3 \cdot 2 - b \cdot 7}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Multiply $2$ by $2$ .

$\frac{4 b - 3 \cdot 2 - b \cdot 7}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Multiply $- 3$ by $2$ .

$\frac{4 b - 6 - b \cdot 7}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Multiply $7$ by $- 1$ .

$\frac{4 b - 6 - 7 b}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Subtract $7 b$ from $4 b$ .

$\frac{- 3 b - 6}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Factor $3$ out of $- 3 b - 6$ .

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

$\frac{3 (- b) - 6}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Factor $3$ out of $- 6$ .

$\frac{3 (- b) + 3 (- 2)}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Factor $3$ out of $3 (- b) + 3 (- 2)$ .

$\frac{3 (- b - 2)}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Simplify terms.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{3 (- b - 2)}{14} \cdot 14 = \frac{b + 3}{14} \cdot 14$

Rewrite the expression.

$3 (- b - 2) = \frac{b + 3}{14} \cdot 14$

Apply the distributive property.

$3 (- b) + 3 \cdot - 2 = \frac{b + 3}{14} \cdot 14$

Multiply.

Multiply $- 1$ by $3$ .

$- 3 b + 3 \cdot - 2 = \frac{b + 3}{14} \cdot 14$

Multiply $3$ by $- 2$ .

$- 3 b - 6 = \frac{b + 3}{14} \cdot 14$

Simplify the right side.

Cancel the common factor of $14$ .

Cancel the common factor.

$- 3 b - 6 = \frac{b + 3}{14} \cdot 14$

Rewrite the expression.

$- 3 b - 6 = b + 3$

Solve for $b$ .

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

Subtract $b$ from both sides of the equation.

$- 3 b - 6 - b = 3$

Subtract $b$ from $- 3 b$ .

$- 4 b - 6 = 3$

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

Add $6$ to both sides of the equation.

$- 4 b = 3 + 6$

Add $3$ and $6$ .

$- 4 b = 9$

Divide each term in $- 4 b = 9$ by $- 4$ and simplify.

Divide each term in $- 4 b = 9$ by $- 4$ .

$\frac{- 4 b}{- 4} = \frac{9}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 b}{- 4} = \frac{9}{- 4}$

Divide $b$ by $1$ .

$b = \frac{9}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$b = - \frac{9}{4}$

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{9}{4}$

Decimal Form:

$b = - 2.25$

Mixed Number Form:

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

Solve for b (2b-3)/7-b/2=(b+3)/14

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