Evaluate (7/2b-3)-(8+6b)

$(\frac{7}{2} b - 3) - (8 + 6 b)$

Step 1

Simplify each term.

Combine $\frac{7}{2}$ and $b$ .

$\frac{7 b}{2} - 3 - (8 + 6 b)$

Apply the distributive property.

$\frac{7 b}{2} - 3 - 1 \cdot 8 - (6 b)$

Multiply $- 1$ by $8$ .

$\frac{7 b}{2} - 3 - 8 - (6 b)$

Multiply $6$ by $- 1$ .

$\frac{7 b}{2} - 3 - 8 - 6 b$

Step 2

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

$\frac{7 b}{2} - 6 b \cdot \frac{2}{2} - 3 - 8$

Step 3

Combine $- 6 b$ and $\frac{2}{2}$ .

$\frac{7 b}{2} + \frac{- 6 b \cdot 2}{2} - 3 - 8$

Step 4

Combine the numerators over the common denominator.

$\frac{7 b - 6 b \cdot 2}{2} - 3 - 8$

Step 5

Find the common denominator.

Write $- 3$ as a fraction with denominator $1$ .

$\frac{7 b - 6 b \cdot 2}{2} + \frac{- 3}{1} - 8$

Multiply $\frac{- 3}{1}$ by $\frac{2}{2}$ .

$\frac{7 b - 6 b \cdot 2}{2} + \frac{- 3}{1} \cdot \frac{2}{2} - 8$

Multiply $\frac{- 3}{1}$ by $\frac{2}{2}$ .

$\frac{7 b - 6 b \cdot 2}{2} + \frac{- 3 \cdot 2}{2} - 8$

Write $- 8$ as a fraction with denominator $1$ .

$\frac{7 b - 6 b \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{- 8}{1}$

Multiply $\frac{- 8}{1}$ by $\frac{2}{2}$ .

$\frac{7 b - 6 b \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{- 8}{1} \cdot \frac{2}{2}$

Multiply $\frac{- 8}{1}$ by $\frac{2}{2}$ .

$\frac{7 b - 6 b \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{- 8 \cdot 2}{2}$

Step 6

Combine the numerators over the common denominator.

$\frac{7 b - 6 b \cdot 2 - 3 \cdot 2 - 8 \cdot 2}{2}$

Step 7

Simplify each term.

Multiply $2$ by $- 6$ .

$\frac{7 b - 12 b - 3 \cdot 2 - 8 \cdot 2}{2}$

Multiply $- 3$ by $2$ .

$\frac{7 b - 12 b - 6 - 8 \cdot 2}{2}$

Multiply $- 8$ by $2$ .

$\frac{7 b - 12 b - 6 - 16}{2}$

Step 8

Simplify terms.

Subtract $12 b$ from $7 b$ .

$\frac{- 5 b - 6 - 16}{2}$

Subtract $16$ from $- 6$ .

$\frac{- 5 b - 22}{2}$

Factor $- 1$ out of $- 5 b$ .

$\frac{- (5 b) - 22}{2}$

Rewrite $- 22$ as $- 1 (22)$ .

$\frac{- (5 b) - 1 (22)}{2}$

Factor $- 1$ out of $- (5 b) - 1 (22)$ .

$\frac{- (5 b + 22)}{2}$

Simplify the expression.

Rewrite $- (5 b + 22)$ as $- 1 (5 b + 22)$ .

$\frac{- 1 (5 b + 22)}{2}$

Move the negative in front of the fraction.

$- \frac{5 b + 22}{2}$

Evaluate (7/2b-3)-(8+6b)

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