How many integers x satisfy - 2 < 4 + 3x < 2?

First, let's solve the inequality:

Subtracting 4 from all 3 terms, we get - 6 < 3x < - 2

Solving - 6 - 2, and solving 3x < - 2 results in x < - 2/3.

Ask: which integers satisfy x>-2? Answers: - 1, 0, 1, 2, ...

Also ask: which integers satisfy x < - 2/3? Answers: - 5, - 4, - 3, - 2, - 1

Notice that the only integer that is found in both sets of possibilities is - 1. So, only one integer x satisfies the given inequality.