Let's determine the value of the expression \(3ab + 5b - 6\) given the values \(a = -1\) and \(b = 3\).
We start by substituting \(a = -1\) and \(b = 3\) into the expression \(3ab + 5b - 6\):
1. Substituting the values:
[tex]\[
3(-1)(3) + 5(3) - 6
\][/tex]
2. Simplifying inside the parentheses and performing the multiplication:
[tex]\[
3 \cdot (-1) \cdot 3 = -9
\][/tex]
3. So, now the expression becomes:
[tex]\[
-9 + 5 \cdot 3 - 6
\][/tex]
4. Next, we handle the multiplication:
[tex]\[
5 \cdot 3 = 15
\][/tex]
5. Now, substitute back into the expression:
[tex]\[
-9 + 15 - 6
\][/tex]
6. Finally, we perform the addition and subtraction from left to right:
[tex]\[
-9 + 15 = 6
\][/tex]
[tex]\[
6 - 6 = 0
\][/tex]
Therefore, the value of the expression [tex]\(3ab + 5b - 6\)[/tex] when [tex]\(a = -1\)[/tex] and [tex]\(b = 3\)[/tex] is [tex]\(\boxed{0}\)[/tex].
