To solve the inequality [tex]\(5 > r - 3\)[/tex], let's go through a step-by-step process:
1. Write down the given inequality:
[tex]\[ 5 > r - 3 \][/tex]
2. Isolate [tex]\(r\)[/tex] on one side of the inequality:
- To isolate [tex]\(r\)[/tex], we need to get rid of [tex]\(-3\)[/tex] on the right-hand side. We can do this by adding [tex]\(3\)[/tex] to both sides of the inequality.
3. Perform the addition on both sides:
[tex]\[ 5 + 3 > r - 3 + 3 \][/tex]
4. Simplify the inequality:
- The [tex]\(-3\)[/tex] and [tex]\(+3\)[/tex] on the right-hand side cancel each other out, leaving:
[tex]\[ 8 > r \][/tex]
5. Rewriting the inequality:
[tex]\[ r < 8 \][/tex]
This simplified form tells us that [tex]\(r\)[/tex] must be less than 8. Therefore, the correct answer is:
A. [tex]\(r < 8\)[/tex]
