Questions: Fill in the blank. The ordered pair (4,7) is a/an of the inequality x+y>2 because when 4 is substituted for and 7 is substituted for the true statement is obtained.

Fill in the blank.
The ordered pair (4,7) is a/an of the inequality x+y>2 because when 4 is substituted for and 7 is substituted for the true statement is obtained.

Transcript text: Fill in the blank. The ordered pair $(4,7)$ is a/an $\square$ of the inequality $\mathrm{x}+\mathrm{y}>2$ because when 4 is substituted for $\square$ and 7 is substituted for $\square$ the true statement $\square$ is obtained.

Solution

Solution Steps

To determine the nature of the ordered pair (4,7) with respect to the inequality $ x + y > 2 $, we need to substitute $ x = 4 $ and $ y = 7 $ into the inequality and check if the resulting statement is true. If the statement is true, then the ordered pair is a solution of the inequality.

Solution Approach

Substitute $ x = 4 $ and $ y = 7 $ into the inequality $ x + y > 2 $.
Check if the resulting statement is true.
If true, the ordered pair is a solution of the inequality.

Step 1: Substitute Values

We start by substituting the values of the ordered pair $ (4, 7) $ into the inequality $ x + y > 2 $. Here, we let $ x = 4 $ and $ y = 7 $.

Step 2: Evaluate the Inequality

Next, we evaluate the left side of the inequality: \[ x + y = 4 + 7 = 11 \] Now we compare this result to the right side of the inequality: \[ 11 > 2 \] This statement is true.

Step 3: Conclusion

Since the statement $ 11 > 2 $ is true, we conclude that the ordered pair $ (4, 7) $ is indeed a solution of the inequality $ x + y > 2 $.

Final Answer

The ordered pair $ (4, 7) $ is a solution of the inequality $ x + y > 2 $ because when $ 4 $ is substituted for $ x $ and $ 7 $ is substituted for $ y $, the true statement $ 11 > 2 $ is obtained. Thus, the answer is $\boxed{\text{solution}}$.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!