Which of the following is true? (1 point) Group of answer choices |−6| < 5 |−6| < |5| |−5| < |−6| |−5| < −6
The Correct Answer and Explanation is :
To evaluate the statements, we need to understand the properties of absolute values and the numbers involved:
- (|-6| < 5): The absolute value of (-6) is (6) (since absolute value measures distance from zero). Therefore, this statement translates to (6 < 5), which is false.
- (|-6| < |5|): The absolute value of (-6) is (6), and the absolute value of (5) is also (5). So, this translates to (6 < 5), which is false.
- (|-5| < |-6|): The absolute value of (-5) is (5), and the absolute value of (-6) is (6). Thus, we have (5 < 6), which is true.
- (|-5| < -6): The absolute value of (-5) is (5), while (-6) is simply (-6). This translates to (5 < -6), which is false.
Summary of Results:
- (|-6| < 5): false
- (|-6| < |5|): false
- (|-5| < |-6|): true
- (|-5| < -6): false
Thus, the correct answer is (|-5| < |-6|), which is true.
Explanation of Absolute Values:
Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of direction. For any real number (x), the absolute value is denoted as (|x|).
- For instance, (|-3| = 3) and (|3| = 3), meaning both (-3) and (3) are three units away from zero.
- In the context of inequalities, comparing absolute values can help understand relationships between numbers. Absolute values are always non-negative; therefore, any inequality involving an absolute value and a negative number will typically be false, as in the case of (|-5| < -6).
- The critical takeaway here is recognizing that while absolute values indicate distances, they don’t change the original sign of the number, which can lead to misunderstandings when dealing with inequalities involving negatives.
In summary, understanding the properties of absolute values is essential in evaluating these statements correctly.