Write the inequalities of the region represented on the number plane and contain in ABC?

To write the inequalities of the region represented on the number plane and contained in triangle ABC, we need to consider the coordinates of the vertices of the triangle.

Let A = (x1, y1), B = (x2, y2), and C = (x3, y3).

The inequalities for the region contained in triangle ABC can be written as follows:

For point P(x, y) to be contained in triangle ABC, the following conditions must be satisfied:

1. The point P must be on or below the line passing through A and B:
(y - y1)/(y2 - y1) <= (x - x1)/(x2 - x1)

2. The point P must be on or below the line passing through B and C:
(y - y2)/(y3 - y2) <= (x - x2)/(x3 - x2)

3. The point P must be on or below the line passing through C and A:
(y - y3)/(y1 - y3) <= (x - x3)/(x1 - x3)

These three inequalities define the region contained in triangle ABC on the number plane.

y ≤ x + 1
y ≥ -x + 3
x ≥ 0