Question
Annette's soccer team will play 15 games this season. That is 7 games fewer than 2 times the number of games they played last season. How many games did they play last season. Equation in the form. px + q = r
Answers
GPT-4o mini
Let \( x \) be the number of games Annette's soccer team played last season. According to the problem, the number of games played this season is 15, which is stated to be 7 games fewer than 2 times the number of games played last season.
We can express this relationship in the form of an equation:
\[
2x - 7 = 15
\]
Now, we can rearrange it to the form \( px + q = r \):
1. Add 7 to both sides:
\[
2x = 15 + 7
\]
2. Simplify the right side:
\[
2x = 22
\]
So the equation in the desired form is:
\[
2x - 22 = 0
\]
This can also be expressed as:
\[
2x + (-22) = 0
\]
Here, \( p = 2 \), \( q = -22 \), and \( r = 0 \).
To find out how many games Annette's team played last season, solve \( 2x = 22 \):
\[
x = \frac{22}{2} = 11
\]
Thus, Annette's soccer team played **11 games** last season.
We can express this relationship in the form of an equation:
\[
2x - 7 = 15
\]
Now, we can rearrange it to the form \( px + q = r \):
1. Add 7 to both sides:
\[
2x = 15 + 7
\]
2. Simplify the right side:
\[
2x = 22
\]
So the equation in the desired form is:
\[
2x - 22 = 0
\]
This can also be expressed as:
\[
2x + (-22) = 0
\]
Here, \( p = 2 \), \( q = -22 \), and \( r = 0 \).
To find out how many games Annette's team played last season, solve \( 2x = 22 \):
\[
x = \frac{22}{2} = 11
\]
Thus, Annette's soccer team played **11 games** last season.