Answer:
B. 7
Explanation:
You want the value of b from the choices {5, 7, 8, 10} that will satisfy both inequalities ...
Substitution
You are asked to find the answer by substitution. This means you put the offered value of 'b' into the inequality where 'b' is, then simplify and see if you have a true relation.
A. b=5
In the first inequality, this is ...
2·5 -8 > 5
10 -8 > 5
2 > f . . . . . . . false — not a solution
B. b=7
In the first inequality, this is ...
2·7 -8 > 5
14 -8 > 5
6 > 5 . . . . . . True
In the second inequality, we have ...
3·7 -13 < 9
21 -13 < 9
8 < 9 . . . . . . True — this is the solution you want
The choice b = 7 satisfies both inequalities.
__
Additional comment
We generally find it easier to compare to zero, rather than some constant. In the attached, we evaluated the left-side expressions ...
- 2b -8 -5 > 0
- 3b -13 -9 < 0
The first inequality is true for b = {7, 8, 10}. The second inequality is true for b = {5, 7}. The only value of b that satisfies both inequalities is b=7.
You will notice we also find it easier to try all the choices at once, rather than retype the calculator input for each one.