Sure, let's evaluate the given expression step by step.
The expression we need to evaluate is:
[tex]\[
\frac{3}{2} y - 3 + \frac{5}{3} z
\][/tex]
We are given:
[tex]\[
y = 6 \quad \text{and} \quad z = 3
\][/tex]
First, substitute [tex]\( y \)[/tex] and [tex]\( z \)[/tex] into the expression:
[tex]\[
\frac{3}{2} (6) - 3 + \frac{5}{3} (3)
\][/tex]
Now, calculate each term individually.
1. Calculate [tex]\(\frac{3}{2} (6)\)[/tex]:
[tex]\[
\frac{3}{2} \times 6 = \frac{3 \times 6}{2} = \frac{18}{2} = 9
\][/tex]
2. The second term is simply:
[tex]\[
-3
\][/tex]
3. Calculate [tex]\(\frac{5}{3} (3)\)[/tex]:
[tex]\[
\frac{5}{3} \times 3 = \frac{5 \times 3}{3} = \frac{15}{3} = 5
\][/tex]
Now, put these calculated values back into the expression:
[tex]\[
9 - 3 + 5
\][/tex]
Finally, perform the addition and subtraction:
[tex]\[
9 - 3 = 6
\][/tex]
[tex]\[
6 + 5 = 11
\][/tex]
Therefore, the evaluated value of the expression is:
[tex]\[
\boxed{11}
\][/tex]
