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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

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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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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)!

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