y ≤ x2 + x - 4y < x2 + 2x + 1

The given inequalities are:

1. y ≤ x^2 + x - 4
2. y < x^2 + 2x + 1

Let's solve them step by step:

1. For the first inequality, we can rewrite it as:

   y - x^2 - x + 4 ≤ 0

   This is a quadratic inequality. The solutions of the corresponding equation y - x^2 - x + 4 = 0 are the x-values where the parabola y = x^2 + x - 4 intersects the x-axis.

2. For the second inequality, we can rewrite it as:

   y - x^2 - 2x - 1 < 0

   This is also a quadratic inequality. The solutions of the corresponding equation y - x^2 - 2x - 1 = 0 are the x-values where the parabola y = x^2 + 2x + 1 intersects the x-axis.

The solution to the system of inequalities will be the x-values that satisfy both inequalities.

Please note that without a specific value for y, we cannot find a numerical solution for x.