Questions: Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The statement "x is at most 9" is written x<9. Choose the correct answer below. A. The statement is true because the inequality symbol in the statement means that x can have values no more than 9. B. The statement is false. It should be changed to x ≥ 9. C. The statement is false. It should be changed to x ≤ 9. D. The statement is true because x<9 means that x can be any value starting from negative infinity up to 9.

Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The statement "x is at most 9" is written x<9.

Choose the correct answer below.
A. The statement is true because the inequality symbol in the statement means that x can have values no more than 9.
B. The statement is false. It should be changed to x ≥ 9.
C. The statement is false. It should be changed to x ≤ 9.
D. The statement is true because x<9 means that x can be any value starting from negative infinity up to 9.

Transcript text: Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The statement " $x$ is at most 9 " is written $x<9$. Choose the correct answer below. A. The statement is true because the inequality symbol in the statement means that x can have values no more than 9 . B. The statement is false. It should be changed to $x \geq 9$. C. The statement is false. It should be changed to $\times \leq 9$. D. The statement is true because $\mathrm{x}<9$ means that x can be any value starting from negative infinity up to 9 .

Solution

Solution Steps

Step 1: Analyze the Statement

The statement claims that "$x$ is at most 9" is written as $x < 9$. The phrase "at most" means that $x$ can be equal to 9 or less than 9. Therefore, the correct inequality should include the possibility of $x$ being equal to 9.

Step 2: Evaluate the Options

Option A: This option incorrectly states that $x < 9$ means $x$ can have values no more than 9. However, $x < 9$ excludes the possibility of $x$ being equal to 9.
Option B: This option suggests changing the inequality to $x \geq 9$, which would mean $x$ is greater than or equal to 9. This is incorrect because "at most 9" implies $x$ is less than or equal to 9.
Option C: This option correctly identifies that the inequality should be $x \leq 9$ to include the possibility of $x$ being equal to 9.
Option D: This option incorrectly states that $x < 9$ means $x$ can be any value starting from negative infinity up to 9, but it still excludes $x = 9$.

Step 3: Determine the Correct Answer

The correct inequality for "$x$ is at most 9" is $x \leq 9$. Therefore, the statement is false, and the correct change is to use $x \leq 9$.