Final answer:
The smallest integer value that satisfies the inequality is 16.
Step-by-step explanation:
To find the smallest integer value that satisfies the inequality, we need to solve the inequality and determine the range of values for x. The inequality is 8 < 5 + 2/5(-x-3/2). Let's simplify the expression:
8 < 5 + 2/5(-x-3/2)
8 < 5 - 2/5x - 3/5
Now, let's combine like terms:
8 < 2/5x + 2
Subtracting 2 from both sides gives us:
6 < 2/5x
Multiplying both sides by 5/2 (or 2.5) gives us:
15 < x
This means that the smallest integer value that satisfies the inequality is 16.