To determine which statement is true about the value of [tex]\( |-14| \)[/tex], let's break down the problem step by step.
1. Calculate the Absolute Value [tex]\( |-14| \)[/tex]:
- The absolute value of a number is defined as its distance from 0 on the number line without considering the direction.
- Mathematically, [tex]\( |-14| = 14 \)[/tex].
2. Evaluate the Given Statements:
- Statement 1: [tex]\( |-14| = -14 \)[/tex]:
- This statement is false because the absolute value of -14 is 14, not -14.
- Statement 2: [tex]\( |-14| < 14 \)[/tex]:
- This statement is false because [tex]\( |-14| = 14 \)[/tex] which is equal to 14, not less than 14.
- Statement 3: It is the distance between -14 and 0 on the number line.
- This statement is true. The distance between -14 and 0 is [tex]\( |-14| \)[/tex], which is 14.
- Statement 4: It is the distance between -14 and 14 on the number line.
- To find the distance between -14 and 14, we calculate [tex]\(|-14 - 14|\)[/tex].
- This simplifies to [tex]\(|-28|\)[/tex], which equals 28.
- Thus, the statement is false as the distance is actually 28.
3. Conclusion:
- The only true statement from the given options is:
- "It is the distance between -14 and 0 on the number line."
Therefore, the true statement is the third one.
