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

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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.

Calculate the left side of the equation: $|-5| * |6|$. Since $|-5| = 5$ and $|6| = 6$, multiply these two values to get \$5 * 6$.

Calculate the right side of the equation: $|-5 * 6|$. First, multiply $-5$ and $6$ to get $-30$, then find the absolute value $|-30|$.

Compare the results from the left side and the right side to see if they are equal.

Conclude whether the statement $|-5| * |6| = |-5*6|$ is true or false based on the comparison.

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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, 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.

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