Is the inequality |-14| < |11| correct?
Understand the Problem
The question presents an inequality involving absolute values and asks for the correctness of a statement about the inequality. However, the inequality provided, [-14]<[11], is unclear due to the square brackets around the numbers. I will assume these are meant to be absolute value signs, making the inequality |-14| < |11|. The task is to evaluate this inequality.
Answer
The statement $|-14| < |11|$ is false.
Answer for screen readers
The statement $|-14| < |11|$ is false.
Steps to Solve
- Evaluate the absolute value of -14
The absolute value of a number is its distance from zero. Thus, the absolute value of $-14$ is $14$.
$|-14| = 14$
- Evaluate the absolute value of 11
Similarly, the absolute value of $11$ is $11$.
$|11| = 11$
- Substitute the absolute values back into the inequality
Replace $|-14|$ with $14$ and $|11|$ with $11$ in the original inequality:
$14 < 11$
- Determine if the inequality is true or false
Compare the two numbers: $14$ is greater than $11$. Therefore, the inequality $14 < 11$ is false.
The statement $|-14| < |11|$ is false.
More Information
The absolute value of a number is its distance from zero on the number line, and it is always non-negative.
Tips
A common mistake is to miscalculate the absolute value of a negative number or to misunderstand the meaning of the absolute value. Another mistake is to reverse the inequality sign when evaluating absolute values.
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