An inequality with absolute values is shown below.

Question

|-14|<|11|

Which statement about the inequality is correct?

A.
The inequality is false because –14 is greater than –11.

B.
The inequality is true because –11 is greater than –14.

C.
The inequality is false because 11 is less than 14.

D.
The inequality is true because 11 is less than 14.

Answer 1

To evaluate the inequality \(|-14| < |11|\), we first need to calculate the absolute values:

\[ |-14| = 14 \] \[ |11| = 11 \]

Now we can rewrite the inequality:

\[ 14 < 11 \]

This statement is false. Now, let's analyze the answer choices:

A. The inequality is false because –14 is greater than –11.

• This is incorrect because we are comparing absolute values, not the original values.

B. The inequality is true because –11 is greater than –14.

• This is incorrect because, again, we need to compare absolute values.

C. The inequality is false because 11 is less than 14.

• This is correct; 11 is indeed less than 14.

D. The inequality is true because 11 is less than 14.

• This is incorrect because the statement says the inequality is true when it is actually false.

Therefore, the correct answer is:

C. The inequality is false because 11 is less than 14.