Question
\begin{tabular}{|l|l|}\hline (a) \( |5-7|=\square \) \\ (b) \( |5|-7=\square \)\end{tabular}
Ask by West Barnett. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
**(a)** \( |5-7| = 2 \)
**(b)** \( |5| - 7 = -2 \)
Solution
**(a)**
1. Compute the expression inside the absolute value:
\[
5 - 7 = -2
\]
2. Take the absolute value of \(-2\):
\[
|-2| = 2
\]
3. Therefore,
\[
|5-7| = 2
\]
**(b)**
1. Compute the absolute value of \(5\):
\[
|5| = 5
\]
2. Subtract \(7\) from \(5\):
\[
5 - 7 = -2
\]
3. Therefore,
\[
|5| - 7 = -2
\]
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Simplify this solution Beyond the Answer
The expression \( |5-7| \) calculates the absolute difference between 5 and 7, which is \( |-2| = 2 \). So, for part (a), the answer is \( 2 \). On the other hand, in part (b), \( |5| - 7 \) first evaluates the absolute value of 5, which is 5. Then, subtracting 7 gives us \( 5 - 7 = -2 \). Therefore, the answer for part (b) is \( -2 \).
