First, let's isolate the variable by adding 1 to all parts of the inequality:

-7 + 1 < 4x - 1 + 1 < 3 + 1

Simplify:

-6 < 4x < 4

Now, divide by 4 to solve for x:

-6/4 < 4x/4 < 4/4

-3/2 < x < 1

Therefore, the solution to the inequality is -3/2 < x < 1.