To solve this inequality, we need to consider the three separate inequalities:

1) -5/2 < 3/x
2) 3/x < 2/-3
3) -5/2 < 2/-3

Let's solve each one individually:

1) -5/2 < 3/x

To get rid of the fraction, we can multiply both sides of the inequality by x:

-5/2 * x < 3

Multiplying both sides by 2 to eliminate the fraction:

-5x < 6

Dividing both sides by -5, remembering to reverse the inequality sign:

x > -6/5

So the first inequality is x > -6/5.

2) 3/x < 2/-3

To eliminate the fraction, we can cross-multiply:

3 * -3 < 2 * x

-9 < 2x

Dividing both sides by 2:

-9/2 < x

So the second inequality is x > -9/2.

3) -5/2 < 2/-3

To eliminate the fraction, we can cross-multiply:

-5 * -3 < 2 * 2

15 < 4

This inequality is not true, so there is no solution for the third inequality.

Combining the solutions from the first two inequalities, we have:

x > -6/5 and x > -9/2

Since x must satisfy both conditions, we can take the larger value, which is x > -6/5.

Therefore, the solution to the inequality -5/2 < 3/x < 2/-3 is x > -6/5.