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

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.