Question

PLEASE HELP me with this problem

Answer 1

Answer: Choice B
The graph with closed circles at 0, 1, 2, 3, 4, 5, and 6

---------------------------------------------------------------

Let x be the number of games in which Jana scored exactly 2 goals
The values of x that are allowed are positive whole numbers only. We cannot have a fractional count of games. We cannot have a negative number of games either.

This season she scored 0 goals in 22 games and 1 goal in each of 16 games. So far, the total comes to 0*22 + 1*16 = 16 goals

For the other games where she scored 2 goals a game, she adds on 2*x goals to the previous total of 16 (eg: if x = 4 then she scores 2*x = 2*4 = 8 extra goals on top of the 16 done so far)

The grand total for this season is 16+2x or 2x+16

This expression 2x+16 must be less than 29 since she scored fewer than the goal count the last season (29). 
Also, the expression 2x+16 must be larger than 16 or equal to 16 because we already know Jana scored 16 goals

What we end up with is this compound inequality: 16 <= 2x+16 < 29 

Let's solve for x
16 <= 2x+16 < 29
16-16 <= 2x+16-16 < 29-16 .... subtract 16 from all sides
0 <= 2x < 13 
0/2 <= 2x/2 < 13/2  .... divide all sides by 2
0 <= x < 6.5

Keep in mind that x is the number of games where exactly two goals are scored by Jana. So we cannot have x = 6.5
Round down to the nearest whole number and we have 0 <= x <= 6
Since x is an integer, we can summarize all the possible x values to be this set of numbers: {0, 1, 2, 3, 4, 5, 6}

Graphing all that on the number line leads to choice B as the answer