Question

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

Answer 1

First, let's solve the inequality:

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

Solving -6 < 3x results in x>-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.