In Exercises 51–60, rewrite each expression without absolute value bars. |12 - π|
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Identify the expression inside the absolute value bars: $12 - \pi$.
Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative.
Determine if the expression inside the absolute value bars is positive or negative. Since $\pi \approx 3.14$, $12 - \pi$ is positive.
Since $12 - \pi$ is positive, the absolute value bars can be removed without changing the expression.
Rewrite the expression without absolute value bars: $12 - \pi$.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value is a mathematical function that measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0. This concept is crucial for understanding how to rewrite expressions that involve absolute values.
A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the main function's domain. When rewriting expressions with absolute values, it is often useful to express them as piecewise functions, which clearly delineate the conditions under which each part of the function applies. This helps in understanding how to handle different cases based on the input value.
Inequalities are mathematical statements that describe the relative size or order of two values. When dealing with absolute values, it is important to set up inequalities to determine the conditions under which the expression inside the absolute value is positive or negative. This understanding is essential for correctly rewriting expressions without absolute value bars.