To solve the given problem, we will evaluate the expression [tex]\(6a + 2b - 3a + 4b - 3\)[/tex] step-by-step using the provided values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the expression:
[tex]\[
6(3) + 2(2) - 3(3) + 4(2) - 3
\][/tex]
2. Calculate each term separately:
[tex]\[
6 \cdot 3 = 18
\][/tex]
[tex]\[
2 \cdot 2 = 4
\][/tex]
[tex]\[
-3 \cdot 3 = -9
\][/tex]
[tex]\[
4 \cdot 2 = 8
\][/tex]
[tex]\[
-3 = -3
\][/tex]
3. Substitute these values back into the expression:
[tex]\[
18 + 4 - 9 + 8 - 3
\][/tex]
4. Perform the additions and subtractions sequentially:
[tex]\[
18 + 4 = 22
\][/tex]
[tex]\[
22 - 9 = 13
\][/tex]
[tex]\[
13 + 8 = 21
\][/tex]
[tex]\[
21 - 3 = 18
\][/tex]
So, the final result after evaluating the expression is:
[tex]\[
18
\][/tex]
Thus, the sum of [tex]\(6a + 2b - 3a + 4b - 3\)[/tex] when [tex]\(a = 3\)[/tex] and [tex]\(b = 2\)[/tex] is [tex]\(\boxed{18}\)[/tex].
