Determine whether each statement is true or false. |-5| ∙ |6| = |-5∙6|

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. Calculate the left side of the equation: \(|-5| * |6|\). Since \(|-5| = 5\) and \(|6| = 6\), multiply these two values to get \$5 * 6$.
3. Calculate the right side of the equation: \(|-5 * 6|\). First, multiply \(-5\) and \$6\( to get \)-30\(, then find the absolute value \)|-30|$.
4. Compare the results from the left side and the right side to see if they are equal.
5. Conclude whether the statement \(|-5| * |6| = |-5*6|\) is true or false based on the comparison.

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |-5| equals 5, and |6| equals 6, regardless of the original sign of the number.

Properties of Absolute Value

One key property is that the absolute value of a product equals the product of the absolute values: |a * b| = |a| * |b|. This means multiplying inside the absolute value or multiplying the absolute values separately yields the same result.

Evaluating Expressions with Absolute Values

To evaluate expressions like |-5| * |6| and |-5*6|, compute each absolute value first, then perform multiplication. This step-by-step approach helps verify if the equality holds true by comparing both sides.