Determine whether each statement is true or false. |-14| / |2| = |-14/2|

Verified step by step guidance

1. Recall the definition of absolute value: for any real number \(x\), \(|x|\) represents the distance of \(x\) from zero on the number line, and it is always non-negative.
2. Evaluate the left side of the equation: calculate \(|-14|\) and \(|2|\) separately. Since absolute value makes numbers positive, \(|-14| = 14\) and \(|2| = 2\).
3. Divide the absolute values on the left side: compute \(\frac{|-14|}{|2|} = \frac{14}{2}\).
4. Evaluate the right side of the equation: calculate the absolute value of the quotient \(\left| \frac{-14}{2} \right|\). First, divide \(-14\) by \(2\) to get \(-7\), then find \(|-7|\).
5. Compare the results from the left and right sides to determine if the equation \(\frac{|-14|}{|2|} = \left| \frac{-14}{2} \right|\) holds true.

Key Concepts

Absolute Value Definition

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |−14| equals 14 because distance is positive regardless of direction.

Properties of Absolute Value with Division

The absolute value of a quotient equals the quotient of the absolute values: |a/b| = |a| / |b|, provided b ≠ 0. This property allows simplification of expressions involving division inside absolute values.

Evaluating Expressions Step-by-Step

To determine the truth of an equation involving absolute values, evaluate each side separately using the definitions and properties, then compare results. This method ensures accurate verification of statements.