4 + (1 + x) = 1 First Step: (4+1) + x = 1 tive property of multiplication over addition ication property of equality tive property of addition tive property of multiplication
4 + (1 + x) = 1 First Step: (4+1) + x = 1 tive property of multiplication over addition ication property of equality tive property of addition tive 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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![### Educational Content on Elementary Algebraic Properties
**Algebraic Equation and Properties**
**Problem:**
\[ 4 + (1 + x) = 1 \]
**First Step:**
\[ (4 + 1) + x = 1 \]
**Question:**
Identify the property used in transforming the equation in the 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
**Answer Choice Section:**
- O Distributive property of multiplication over addition
- O Multiplication property of equality
- O Associative property of addition
- O Associative property of multiplication
**Submit Answer Button:**
A button labeled "Submit Answer."
**Website Footer:**
- **Privacy Policy**
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---
### Explanation of Concepts
1. **Distributive Property of Multiplication over Addition:**
The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products.
\[ a(b + c) = ab + ac \]
2. **Multiplication Property of Equality:**
This property states that when both sides of an equation are multiplied by the same non-zero number, the sides remain equal.
\[ a = b \Rightarrow ac = bc \]
3. **Associative Property of Addition:**
The associative property of addition states that the way in which numbers are grouped in addition does not change their sum.
\[ (a + b) + c = a + (b + c) \]
4. **Associative Property of Multiplication:**
The associative property states that the way in which numbers are grouped in multiplication does not change their product.
\[ (ab)c = a(bc) \]
**In this Problem:**
The associative property of addition is used in the first step:
\[ 4 + (1 + x) = (4 + 1) + x \]
Encourage students to identify the associative property of addition in transforming the equation by rearranging the grouping of numbers in the sum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9503a69-18de-481a-b8ce-3188f24c3606%2F12afce0c-cecc-46dd-9adf-cf4e4f22ab1d%2Ftqyddnq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content on Elementary Algebraic Properties
**Algebraic Equation and Properties**
**Problem:**
\[ 4 + (1 + x) = 1 \]
**First Step:**
\[ (4 + 1) + x = 1 \]
**Question:**
Identify the property used in transforming the equation in the 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
**Answer Choice Section:**
- O Distributive property of multiplication over addition
- O Multiplication property of equality
- O Associative property of addition
- O Associative property of multiplication
**Submit Answer Button:**
A button labeled "Submit Answer."
**Website Footer:**
- **Privacy Policy**
- **Terms of Service**
**Copyright Information:**
© 2023 DeltaMath.com. All Rights Reserved.
---
### Explanation of Concepts
1. **Distributive Property of Multiplication over Addition:**
The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products.
\[ a(b + c) = ab + ac \]
2. **Multiplication Property of Equality:**
This property states that when both sides of an equation are multiplied by the same non-zero number, the sides remain equal.
\[ a = b \Rightarrow ac = bc \]
3. **Associative Property of Addition:**
The associative property of addition states that the way in which numbers are grouped in addition does not change their sum.
\[ (a + b) + c = a + (b + c) \]
4. **Associative Property of Multiplication:**
The associative property states that the way in which numbers are grouped in multiplication does not change their product.
\[ (ab)c = a(bc) \]
**In this Problem:**
The associative property of addition is used in the first step:
\[ 4 + (1 + x) = (4 + 1) + x \]
Encourage students to identify the associative property of addition in transforming the equation by rearranging the grouping of numbers in the sum.
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