myGalaxyLogon When solving an equation, Anne's first step is shown below. Which property justifies Anne's first step? Original Equation: 4 + (1 + x) = 1 First Step: (4 + 1) + x = 1 WebConnect 3270 distributive property of multiplication over addition multiplication property of equality associative property of addition associative property of multiplication
myGalaxyLogon When solving an equation, Anne's first step is shown below. Which property justifies Anne's first step? Original Equation: 4 + (1 + x) = 1 First Step: (4 + 1) + x = 1 WebConnect 3270 distributive property of multiplication over addition multiplication property of equality associative property of addition associative property of multiplication
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Understanding Mathematical Properties in Equation Solving**
When solving an equation, identifying and applying mathematical properties accurately is crucial. Below is an example of how Anne uses one such property in her first step of solving an equation:
### Original Equation:
\[ 4 + (1 + x) = 1 \]
### First Step:
\[ (4 + 1) + x = 1 \]
### Question:
Which property justifies Anne's first step?
### Options:
1. Distributive property of multiplication over addition
2. Multiplication property of equality
3. Associative property of addition
4. Associative property of multiplication
### Explanation:
In this scenario, Anne is re-grouping the numbers in the equation. Initially, she has the operation \( 4 + (1 + x) \). In her first step, she combines 4 and 1 together inside the parenthesis and then adds x, indicating that she is using the **associative property of addition**.
The associative property of addition states that the way in which numbers are grouped in an addition problem does not change the sum. Mathematically, this means:
\[ (a + b) + c = a + (b + c) \]
Therefore, the correct answer is:
\[ \text{Associative property of addition} \]
---
In summary, understanding and applying properties like the associative property is fundamental in simplifying and solving equations effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9503a69-18de-481a-b8ce-3188f24c3606%2F2ccd09b0-90e0-431d-b15a-6a790cc23a12%2Fd3dvz2p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Mathematical Properties in Equation Solving**
When solving an equation, identifying and applying mathematical properties accurately is crucial. Below is an example of how Anne uses one such property in her first step of solving an equation:
### Original Equation:
\[ 4 + (1 + x) = 1 \]
### First Step:
\[ (4 + 1) + x = 1 \]
### Question:
Which property justifies Anne's first step?
### Options:
1. Distributive property of multiplication over addition
2. Multiplication property of equality
3. Associative property of addition
4. Associative property of multiplication
### Explanation:
In this scenario, Anne is re-grouping the numbers in the equation. Initially, she has the operation \( 4 + (1 + x) \). In her first step, she combines 4 and 1 together inside the parenthesis and then adds x, indicating that she is using the **associative property of addition**.
The associative property of addition states that the way in which numbers are grouped in an addition problem does not change the sum. Mathematically, this means:
\[ (a + b) + c = a + (b + c) \]
Therefore, the correct answer is:
\[ \text{Associative property of addition} \]
---
In summary, understanding and applying properties like the associative property is fundamental in simplifying and solving equations effectively.
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