Write the inequality shown by the shaded region in the graph with the boundary line y = -2x - 5

We do not have the image, so we can answer in a general way.

We know that the boundary line is y = -2*x - 5

We can have 4 cases:

1) a dashed line and the shaded part is above the line.

y >  -2*x - 5

2) a dashed line and the shaded part is below the line

y < -2*x - 5

Here we have dashed lines because the values of the line are not solutions for the inequality.

3) a solid line and the shaded part is above the line.

y ≥  -2*x - 5

4) a solid line and the shaded part is below the line.

y ≤  -2*x - 5

Here we have solid lines because the values in the line itself are solutions.