Rewrite each expression without absolute value bars. |7 - π|

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Recall that the absolute value expression \(|x|\) can be rewritten as a piecewise function: \(|x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases}\).

Identify the expression inside the absolute value bars: \(7 - \pi\).

Determine whether \(7 - \pi\) is nonnegative or negative by comparing the values of 7 and \(\pi\) (approximately 3.14159).

Since \(7 - \pi > 0\), the absolute value expression simplifies to \(7 - \pi\) without the bars.

Therefore, \(|7 - \pi|\) can be rewritten as \(7 - \pi\) because the quantity inside the absolute value is positive.

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주요 개념

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

Absolute Value Definition

The absolute value of a number represents its distance from zero on the number line, always expressed as a non-negative value. For any real number x, |x| equals x if x is non-negative, and -x if x is negative.

Evaluating Expressions Involving Constants

When rewriting expressions without absolute value bars, it is important to evaluate or compare constants like π (approximately 3.14) to determine the sign of the expression inside the absolute value. This helps decide whether to keep the expression as is or negate it.

Piecewise Definition of Absolute Value

Absolute value expressions can be rewritten as piecewise functions that define different outputs depending on the sign of the inner expression. For example, |7 - π| equals 7 - π if 7 - π ≥ 0, otherwise it equals -(7 - π).