List the elements in each set. See Example 1. {p|p is a number whose absolute value is 4}

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Understand the problem: We need to find all numbers \( p \) such that the absolute value of \( p \) is 4. The absolute value of a number is its distance from zero on the number line, regardless of direction.

Recall the definition of absolute value: For any number \( p \), \( |p| = 4 \) means \( p \) can be either 4 or -4 because both have an absolute value of 4.

Write the equation representing the condition: \( |p| = 4 \). This implies two possible equations: \( p = 4 \) or \( p = -4 \).

List the elements of the set by including all values of \( p \) that satisfy the condition: \( \{4, -4\} \).

Verify the solution by checking the absolute value of each element: \( |4| = 4 \) and \( |-4| = 4 \), confirming both satisfy the condition.

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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, regardless of direction. It is always non-negative. For example, the absolute value of both 4 and -4 is 4, denoted as |4| = 4 and |-4| = 4.

Set Notation and Description

Set notation describes a collection of elements that satisfy a specific property. In this question, the set is defined by a condition on its elements, such as all numbers p where |p| = 4. Understanding how to interpret and list elements from such descriptions is essential.

Solving Absolute Value Equations

To find elements satisfying an absolute value equation like |p| = 4, solve for p by considering both positive and negative cases: p = 4 and p = -4. This approach helps identify all possible elements in the set.