Question
The graph shows an inequality that predicts citrus production, where y is the annual production of citrus in thousands of pounds and x is acres of land in thousands. The inequality is "y" less than or equal to 26 "x" minus 6600.y≤26x−6600. Is the ordered pair (400,1000) a solution to this inequality?
Answers
GPT-4o mini
To determine if the ordered pair (400, 1000) is a solution to the inequality \( y \leq 26x - 6600 \), we need to substitute \( x = 400 \) and \( y = 1000 \) into the inequality and see if it holds true.
First, let's calculate the right side of the inequality with \( x = 400 \):
\[
y \leq 26(400) - 6600
\]
Calculating \( 26(400) \):
\[
26 \times 400 = 10400
\]
Now, substituting this back into the inequality:
\[
y \leq 10400 - 6600
\]
Calculating \( 10400 - 6600 \):
\[
10400 - 6600 = 3800
\]
Now, we need to evaluate the inequality \( y \leq 3800 \) with \( y = 1000 \):
\[
1000 \leq 3800
\]
This statement is true, as 1000 is indeed less than or equal to 3800.
Therefore, the ordered pair \( (400, 1000) \) is a solution to the inequality \( y \leq 26x - 6600 \).
First, let's calculate the right side of the inequality with \( x = 400 \):
\[
y \leq 26(400) - 6600
\]
Calculating \( 26(400) \):
\[
26 \times 400 = 10400
\]
Now, substituting this back into the inequality:
\[
y \leq 10400 - 6600
\]
Calculating \( 10400 - 6600 \):
\[
10400 - 6600 = 3800
\]
Now, we need to evaluate the inequality \( y \leq 3800 \) with \( y = 1000 \):
\[
1000 \leq 3800
\]
This statement is true, as 1000 is indeed less than or equal to 3800.
Therefore, the ordered pair \( (400, 1000) \) is a solution to the inequality \( y \leq 26x - 6600 \).