Evaluate Using the Given Value f(6)=3/2(6)-1/2

$f (6) = \frac{3}{2} (6) - \frac{1}{2}$

Step 1

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$f (6) = \frac{3}{2} \cdot (2 (3)) - \frac{1}{2}$

Cancel the common factor.

$f (6) = \frac{3}{2} \cdot (2 \cdot 3) - \frac{1}{2}$

Rewrite the expression.

$f (6) = 3 \cdot 3 - \frac{1}{2}$

Multiply $3$ by $3$ .

$f (6) = 9 - \frac{1}{2}$

Step 2

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$f (6) = 9 \cdot \frac{2}{2} - \frac{1}{2}$

Step 3

Combine $9$ and $\frac{2}{2}$ .

$f (6) = \frac{9 \cdot 2}{2} - \frac{1}{2}$

Step 4

Combine the numerators over the common denominator.

$f (6) = \frac{9 \cdot 2 - 1}{2}$

Step 5

Simplify the numerator.

Multiply $9$ by $2$ .

$f (6) = \frac{18 - 1}{2}$

Subtract $1$ from $18$ .

$f (6) = \frac{17}{2}$