Certainly! To evaluate the expression [tex]\(5r + 7s - 3(r + s) + 4\)[/tex] when [tex]\(r = 2\)[/tex] and [tex]\(s = 3\)[/tex], follow these steps:
1. Substitute the values of [tex]\(r\)[/tex] and [tex]\(s\)[/tex] into the expression:
[tex]\[
5(2) + 7(3) - 3(2 + 3) + 4
\][/tex]
2. Simplify each term separately:
- First term: [tex]\(5(2) = 10\)[/tex]
- Second term: [tex]\(7(3) = 21\)[/tex]
- Third term inside the parenthesis: [tex]\(2 + 3 = 5\)[/tex]
- Third term: [tex]\(3(5) = 15\)[/tex]
So, the expression now looks like:
[tex]\[
10 + 21 - 15 + 4
\][/tex]
3. Combine these results step by step:
- Combine the first two terms: [tex]\(10 + 21 = 31\)[/tex]
- Subtract the third term: [tex]\(31 - 15 = 16\)[/tex]
- Add the fourth term: [tex]\(16 + 4 = 20\)[/tex]
4. Conclusion:
The value of the expression [tex]\(5r + 7s - 3(r + s) + 4\)[/tex] when [tex]\(r = 2\)[/tex] and [tex]\(s = 3\)[/tex] is [tex]\( \boxed{20} \)[/tex].
