Question

Referees of high school soccer games will end a game at half time if a team is ahead or behind by at least 8 goals. During the district championship game, the applewood soccer team had scored 11 goals in the first half. Graph an inequality that represents the possible goals, g, scored by the opposing team if the referees end the game at half time

Answer 1

If at the end of the first half, the difference between the goals scored by the applewood team and the opposing team is greater than or equal to 8, then the referee will finish the game at the end of the first half.

If we call g the number of goals scored by the opposing team, then we can express this situation as an inequality:

$11-g \geq 8\\g \leq 11-8\\g \leq 3$

However, it is impossible for a team to score -1 goal. Therefore the number of goals scored by the opposing team must be a number greater than 0.

So, the inequality is:

$g \leq 3$ and $g \geq 0$

$0 \leq g \leq 3$

The attached figure shows the graph for this inequality, which represents the number of goals that the opposing team could score if the referee finished the game in the first half.