The number of integer values of the argument for which the graph of the function (x)

The number of integer values of the argument for which the graph of the function (x) = | x + 2 | -5 is located below the Ox axis is ….

1. The ordinates of all points of the coordinate plane located below the abscissa axis are negative, therefore, to find the values of the argument that satisfy the condition of the problem, it is necessary to solve the strict inequality:

y (x) = | x + 2 | – 5;
| x + 2 | – 5 <0.
2. Move the number -5 to the right side and rewrite the inequality as a system of two inequalities:

| x + 2 | <5;
{x + 2> -5;
{x + 2 <5;
{x> -5 – 2;
{x <5 – 2;
{x> -7;
{x <3;
x ∈ (-7; 3).
3. This interval includes 9 integer solutions: from -6 to 2.

Answer: 9.