To solve the expression [tex]\(6a + 2b - 3a + 4b - 3\)[/tex] when [tex]\(a = 3\)[/tex] and [tex]\(b = 2\)[/tex], we can break down the problem into a few manageable steps.
1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the expression:
Substitute [tex]\(a = 3\)[/tex] and [tex]\(b = 2\)[/tex] into the expression:
[tex]\[
6(3) + 2(2) - 3(3) + 4(2) - 3
\][/tex]
2. Perform the multiplication for each term:
[tex]\[
6 \cdot 3 = 18
\][/tex]
[tex]\[
2 \cdot 2 = 4
\][/tex]
[tex]\[
3 \cdot 3 = 9
\][/tex]
[tex]\[
4 \cdot 2 = 8
\][/tex]
Thus, the expression now becomes:
[tex]\[
18 + 4 - 9 + 8 - 3
\][/tex]
3. Combine the results step-by-step:
First, add the positive terms:
[tex]\[
18 + 4 + 8 = 30
\][/tex]
Then, subtract the negative terms:
[tex]\[
30 - 9 = 21
\][/tex]
[tex]\[
21 - 3 = 18
\][/tex]
Therefore, the sum of the expression [tex]\(6a + 2b - 3a + 4b - 3\)[/tex] when [tex]\(a = 3\)[/tex] and [tex]\(b = 2\)[/tex] is [tex]\(18\)[/tex].
