To determine which values of [tex]\( b \)[/tex] satisfy the inequality [tex]\( 5 < b - 3 \)[/tex], let's solve the inequality step by step.
1. Start with the given inequality:
[tex]\[
5 < b - 3
\][/tex]
2. Add 3 to both sides of the inequality to isolate [tex]\( b \)[/tex]:
[tex]\[
5 + 3 < b - 3 + 3
\][/tex]
3. Simplify both sides:
[tex]\[
8 < b
\][/tex]
This tells us that [tex]\( b \)[/tex] must be greater than 8.
Let's check each option to see which values of [tex]\( b \)[/tex] satisfy this inequality:
- Option A: [tex]\( b = 8 \)[/tex]
[tex]\[
8 \not> 8
\][/tex]
So, [tex]\( b = 8 \)[/tex] does not satisfy the inequality.
- Option B: [tex]\( b = 9 \)[/tex]
[tex]\[
9 > 8
\][/tex]
Thus, [tex]\( b = 9 \)[/tex] satisfies the inequality.
- Option C: [tex]\( b = 10 \)[/tex]
[tex]\[
10 > 8
\][/tex]
So, [tex]\( b = 10 \)[/tex] also satisfies the inequality.
Based on this analysis, the values of [tex]\( b \)[/tex] that satisfy the inequality [tex]\( 5 < b - 3 \)[/tex] are:
B) [tex]\( b = 9 \)[/tex]
C) [tex]\( b = 10 \)[/tex]
