22. What is the average(arithmetic mean) of all the integers
from -39 to 40, inclusive?

This range contains 80 numbers (40 in 1-40, and another 40 in -39-0).

We have

S = 1 + 2 + 3 + … + 38 + 39 + 40

S = 40 + 39 + 38 + … + 3 + 2 + 1

==>   2S = (1 + 40) + (2 + 39) + … + (39 + 2) + (40 + 1)

==>   2S = 40 × 41

==>   S = 820

and

T = 0 + 1 + 2 + … + 37 + 38 + 39

T = 39 + 38 + 37 + … + 3 + 2 + 1

==>   2T = (0 + 39) + (1 + 38) + … + (38 + 2) + (39 + 0)

==>   2T = 40 × 39

==>   T = 780

The average of the numbers in this range is equal to the total divided by the amount of numbers in the range, so

average = (40 + 39 + … + 1 + 0 + (-1) + … + (-38) + (-39))/80

average = (S - T )/80

average = (820 - 780)/80

average = 40/80 = 1/2

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!