The equation \(|2x + 1| + |y - 1| = 4\) represents a geometric figure in the coordinate plane. This equation describes a diamond (or rhombus) shape centered at the point \((-0.5, 1)\).

To understand the boundaries, we can analyze the cases based on the signs of the expressions inside the absolute values.

1. **Case 1**: \(2x + 1 \geq 0\) and \(y - 1 \geq 0\)
- The equation simplifies to \(2x + 1 + y - 1 = 4 \Rightarrow 2x + y = 4\).

2. **Case 2**: \(2x + 1 \geq 0\) and \(y - 1 < 0\)
- The equation becomes \(2x + 1 - (y - 1) = 4 \Rightarrow 2x - y + 2 = 4 \Rightarrow 2x - y = 2\).

3. **Case 3**: \(2x + 1 < 0\) and \(y - 1 \geq 0\)
- The equation rewrites to \(-(2x + 1) + (y - 1) = 4 \Rightarrow -2x + y - 2 = 4 \Rightarrow -2x + y = 6\).

4. **Case 4**: \(2x + 1 < 0\) and \(y - 1 < 0\)
- The equation is \(-(2x + 1) - (y - 1) = 4 \Rightarrow -2x - y + 2 = 4 \Rightarrow -2x - y = 2\).

The lines represented by these equations form the boundary of the diamond:

- \(y = 4 - 2x\)
- \(y = 2x + 2\)
- \(y = -2x + 6\)
- \(y = -2x - 2\)

The vertices of the diamond can be found by solving the intersections of these lines. The four intersection points will give the corners of the diamond shape, representing the solution set of the original equation.