To model the scenario given by the equation [tex]\(\frac{x}{5} - 2 = 11\)[/tex], we can take the following steps to solve for [tex]\(x\)[/tex]:
### Step-by-Step Solution:
1. Start with the given equation:
[tex]\[
\frac{x}{5} - 2 = 11
\][/tex]
2. Isolate the fractional term by adding 2 to both sides:
[tex]\[
\frac{x}{5} - 2 + 2 = 11 + 2
\][/tex]
Simplifying this:
[tex]\[
\frac{x}{5} = 13
\][/tex]
3. Eliminate the fraction by multiplying both sides by 5:
[tex]\[
\left(\frac{x}{5}\right) \cdot 5 = 13 \cdot 5
\][/tex]
Simplifying this:
[tex]\[
x = 65
\][/tex]
So, [tex]\(x\)[/tex], the number of basketball players that have signed up for the league, is 65.
### Interpretation:
Now, let's consider a possible scenario that would be modeled by this equation.
The term [tex]\(\frac{x}{5}\)[/tex] suggests that the total number of players, [tex]\(x\)[/tex], might be divided into groups or teams of 5 players each. The equation further suggests that when 2 players are subtracted from each group, there would still be enough players left to form 11 complete teams (since [tex]\(\frac{x}{5} - 2 = 11\)[/tex]).
Here’s a practical scenario:
- Suppose each group or team originally has 5 players.
- If 2 players are removed from each team, the remaining number of players still forms 11 complete teams.
- This leads to the conclusion that beyond these adjustments, there were indeed 65 players to begin with (since [tex]\(x = 65\)[/tex]).
Thus, the scenario represents a situation where:
- A basketball league has 65 players signed up.
- These players are typically divided into teams of 5.
- After adjusting by removing 2 players per team, you are left with 11 full teams.
This mathematical and scenario-based analysis matches the given principles explained within the context, showing that 65 is the correct number of basketball players accounting for the conditions given in the equation.
