Determine whether each statement is true or false. |25| = |-25|
Verified step by step guidance
1
Understand the concept of absolute value: The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.
Calculate the absolute value of 25: \(|25| = 25\) because 25 is already a positive number.
Calculate the absolute value of -25: \(|-25| = 25\) because the absolute value makes the negative number positive.
Compare the two absolute values: Since both \(|25|\) and \(|-25|\) equal 25, they are equal.
Conclude that the statement \(|25| = |-25|\) is true because both sides of the equation are equal.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |5| equals 5, and |-5| also equals 5, indicating that both numbers are the same distance from zero.
One key property of absolute values is that |a| = |b| if and only if a = b or a = -b. This means that two numbers can have the same absolute value if one is the negative of the other. This property is essential for comparing absolute values in equations or inequalities.
When comparing the absolute values of two numbers, such as |25| and |-25|, we can determine their equality by evaluating each expression. Since both expressions yield the same result (25), we conclude that the statement is true, demonstrating that absolute values eliminate the effect of negative signs.