Problem 54 - Algebra and Trigonometry

Question

Rewrite each expression without absolute value bars. $$|7-\pi|$$

Step-by-Step Solution

Answer

The expression \(|7-\pi|\) without absolute-value bars is 3.8584.

Step 1: Understanding the absolute value

The absolute value of a number can be understood as its distance from 0 on the number line. It means that regardless of the sign (+/-), the value will always be positive. Hence, \(|7-\pi|\) is tantamount to determining the distance between 7 and \(\pi\) on the number line.

Step 2: Calculating the Difference

Calculate the difference between 7 and \(\pi\). Performing this operation we find \(7-\pi \approx 7-3.1416 = 3.8584\). Notice that the result is a positive number which tells us our calculation is correct because absolute value can never be negative.

Step 3: Writing the Result without Absolute-Value Bars

Now write the result without the absolute-value bars. The absolute value of \(7-\pi\) which we computed in Step 2 is equivalent to 3.8584.