which can be rewritten
Squaring both sides,
That is the straight line through (0, -1) and (-1, 0). But in order that the left side be a real number (so it can be compared to 1) we must have or . is a parabola. for (x, y) below that parabola.
If x= 0, y= 0, the original inequality is 0< 1 which is true. That means that all (x, y) on the same side of y= -x- 1 as (0, 0) (above and to the right) satisfy the inequality provided they also lie below the parabola. The line and parabola do NOT intersect so that is not anything like a "triangle"- it is and unbounded region.