Question
Elntegers and Rational Numbers Operations with absolute value: Problem type 1 Evaluate the following, (a) \( |-4|+9=\square \) (b) \( |-4+9|=\square \)
Ask by Montgomery Vaughan. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) \( |-4| + 9 = 13 \)
(b) \( |-4 + 9| = 5 \)
Solution
Let's evaluate each expression step by step.
### (a) \( |-4| + 9 \)
1. **Calculate the absolute value**: The absolute value of \(-4\) is \(4\). This is because the absolute value function returns the non-negative value of a number.
\[
|-4| = 4
\]
2. **Add \(9\)**: Now, we add \(4\) to \(9\).
\[
4 + 9 = 13
\]
So, the answer for part (a) is:
\[
|-4| + 9 = 13
\]
### (b) \( |-4 + 9| \)
1. **Calculate the expression inside the absolute value**: First, we need to evaluate \(-4 + 9\).
\[
-4 + 9 = 5
\]
2. **Calculate the absolute value**: The absolute value of \(5\) is \(5\) since it is already a non-negative number.
\[
|5| = 5
\]
So, the answer for part (b) is:
\[
|-4 + 9| = 5
\]
### Final Answers:
(a) \( |-4| + 9 = 13 \)
(b) \( |-4 + 9| = 5 \)
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Simplify this solution Beyond the Answer
Let's break down these absolute value problems! For part (a), when you evaluate \( |-4|+9 \), you first find the absolute value of \(-4\), which is \(4\). So, you add \(4 + 9\) to get \(13\). Hence, \( |-4| + 9 = 13 \). Now, for part (b), \( |-4 + 9| \), you first perform the operation inside the absolute value. Adding \(-4 + 9\) yields \(5\). The absolute value of \(5\) is just \(5\), so \( |-4 + 9| = 5 \). So, the answers are \(13\) for part (a) and \(5\) for part (b)!
