Original Equation: 4+ (1+x) = 1 First Step:
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.3: Solving Problems Involving Inequalities
Problem 17P
Related questions
Question
![**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:**
\[(4 + 1) + x = 1\]
- o distributive property of multiplication over addition
- o multiplication property of equality
- o associative property of addition
- o associative property of multiplication
**Explanation:**
In the original equation, \[ 4 + (1 + x) = 1 \], Anne's first step is to rearrange the terms inside the parentheses. She changes it to \[ (4 + 1) + x = 1 \], which is an application of the **associative property of addition**. This property states that the way in which numbers are grouped in addition does not change their sum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9503a69-18de-481a-b8ce-3188f24c3606%2Fa8cd732c-b61c-4887-a20a-92170d9a5cbf%2Fqh05ehb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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:**
\[(4 + 1) + x = 1\]
- o distributive property of multiplication over addition
- o multiplication property of equality
- o associative property of addition
- o associative property of multiplication
**Explanation:**
In the original equation, \[ 4 + (1 + x) = 1 \], Anne's first step is to rearrange the terms inside the parentheses. She changes it to \[ (4 + 1) + x = 1 \], which is an application of the **associative property of addition**. This property states that the way in which numbers are grouped in addition does not change their sum.
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