Answer The following properties are used to prove the given statement: additive property associative property of addition property of opposites Explanation Given information: To prove: If a + a = a , then a = 0 . Steps of proof: 1. a + a = a 2. − a is a real numbers 3. ( a + a ) + ( − a ) = a + ( − a ) 4. a + [ a + ( − a ) ] = a + ( − a ) 5. a + 0 = 0 6. ∴ a = 0 Here, the given proof statement is: If a + a = a , then a = 0 The steps for the proof are also given. Now, need to give the reasons used to proof the given statement are as: a + a = a This is the given statement as per the problem. − a is a real numbers It is given information. ( a + a ) + ( − a ) = a + ( − a ) Here, to proof the given statement there is use of additive property. On the both sides there is addition of ( − a ) . a + [ a + ( − a ) ] = a + ( − a ) The like terms are grouped in this step using the associative property of addition a + 0 = 0 The property of opposites is used in this step to reduce a + ( − a ) to 0 ∴ a = 0 Finally, the expression is reduced in the form of the variable a .

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 2.6, Problem 7OE

To determine

To explain:

The reason for the given proof:

‘If a+a=a , then a=0 .’

Expert Solution & Answer

Answer to Problem 7OE

The following properties are used to prove the given statement:

additive property
associative property of addition
property of opposites

Explanation of Solution

Given information:

To prove:

If a+a=a , then a=0 .

Steps of proof:

1. a+a=a

2. −a is a real numbers

3. (a+a)+(−a)=a+(−a)

4. a+[a+(−a)]=a+(−a)

5. a+0=0

6. ∴a=0

Here, the given proof statement is:

If a+a=a , then a=0

The steps for the proof are also given. Now, need to give the reasons used to proof the given statement are as:

a+a=a

This is the given statement as per the problem.

−a is a real numbers
(a+a)+(−a)=a+(−a)

Here, to proof the given statement there is use of additive property. On the both sides there is addition of (−a) .

a+[a+(−a)]=a+(−a)

The like terms are grouped in this step using the associative property of addition

a+0=0

The property of opposites is used in this step to reduce a+(−a) to 0

∴a=0

Finally, the expression is reduced in the form of the variable a .

Chapter 2.6, Problem 6OE

Chapter 2.6, Problem 8OE

Chapter 2 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 2.1 - Prob. 1OE Ch. 2.1 - Prob. 2OE Ch. 2.1 - Prob. 3OE Ch. 2.1 - Prob. 4OE Ch. 2.1 - Prob. 5OE Ch. 2.1 - Prob. 6OE Ch. 2.1 - Prob. 7OE Ch. 2.1 - Prob. 8OE Ch. 2.1 - Prob. 9OE Ch. 2.1 - Prob. 10OE

Ch. 2.1 - Prob. 11OE Ch. 2.1 - Prob. 12OE Ch. 2.1 - Prob. 13OE Ch. 2.1 - Prob. 14OE Ch. 2.1 - Prob. 15OE Ch. 2.1 - Prob. 16OE Ch. 2.1 - Prob. 17OE Ch. 2.1 - Prob. 1WE Ch. 2.1 - Prob. 2WE Ch. 2.1 - Prob. 3WE Ch. 2.1 - Prob. 4WE Ch. 2.1 - Prob. 5WE Ch. 2.1 - Prob. 6WE Ch. 2.1 - Prob. 7WE Ch. 2.1 - Prob. 8WE Ch. 2.1 - Prob. 9WE Ch. 2.1 - Prob. 10WE Ch. 2.1 - Prob. 11WE Ch. 2.1 - Prob. 12WE Ch. 2.1 - Prob. 13WE Ch. 2.1 - Prob. 14WE Ch. 2.1 - Prob. 15WE Ch. 2.1 - Prob. 16WE Ch. 2.1 - Prob. 17WE Ch. 2.1 - Prob. 18WE Ch. 2.1 - Prob. 19WE Ch. 2.1 - Prob. 20WE Ch. 2.1 - Prob. 21WE Ch. 2.1 - Prob. 22WE Ch. 2.1 - Prob. 23WE Ch. 2.1 - Prob. 24WE Ch. 2.1 - Prob. 25WE Ch. 2.1 - Prob. 26WE Ch. 2.1 - Prob. 27WE Ch. 2.1 - Prob. 28WE Ch. 2.1 - Prob. 29WE Ch. 2.1 - Prob. 30WE Ch. 2.1 - Prob. 31WE Ch. 2.1 - Prob. 32WE Ch. 2.1 - Prob. 33WE Ch. 2.1 - Prob. 1MRE Ch. 2.1 - Prob. 2MRE Ch. 2.1 - Prob. 3MRE Ch. 2.1 - Prob. 4MRE Ch. 2.1 - Prob. 5MRE Ch. 2.1 - Prob. 6MRE Ch. 2.1 - Prob. 7MRE Ch. 2.1 - Prob. 8MRE Ch. 2.1 - Prob. 9MRE Ch. 2.1 - Prob. 10MRE Ch. 2.1 - Prob. 11MRE Ch. 2.1 - Prob. 12MRE Ch. 2.1 - Prob. 1CE Ch. 2.1 - Prob. 2CE Ch. 2.1 - Prob. 3CE Ch. 2.1 - Prob. 4CE Ch. 2.2 - Prob. 1OE Ch. 2.2 - Prob. 2OE Ch. 2.2 - Prob. 3OE Ch. 2.2 - Prob. 4OE Ch. 2.2 - Prob. 5OE Ch. 2.2 - Prob. 6OE Ch. 2.2 - Prob. 7OE Ch. 2.2 - Prob. 8OE Ch. 2.2 - Prob. 9OE Ch. 2.2 - Prob. 10OE Ch. 2.2 - Prob. 11OE Ch. 2.2 - Prob. 12OE Ch. 2.2 - Prob. 13OE Ch. 2.2 - Prob. 14OE Ch. 2.2 - Prob. 1WE Ch. 2.2 - Prob. 2WE Ch. 2.2 - Prob. 3WE Ch. 2.2 - Prob. 4WE Ch. 2.2 - Prob. 5WE Ch. 2.2 - Prob. 6WE Ch. 2.2 - Prob. 7WE Ch. 2.2 - Prob. 8WE Ch. 2.2 - Prob. 9WE Ch. 2.2 - Prob. 10WE Ch. 2.2 - Prob. 11WE Ch. 2.2 - Prob. 12WE Ch. 2.2 - Prob. 13WE Ch. 2.2 - Prob. 14WE Ch. 2.2 - Prob. 15WE Ch. 2.2 - Prob. 16WE Ch. 2.2 - Prob. 17WE Ch. 2.2 - Prob. 18WE Ch. 2.2 - Prob. 19WE Ch. 2.2 - Prob. 20WE Ch. 2.2 - Prob. 21WE Ch. 2.2 - Prob. 22WE Ch. 2.2 - Prob. 23WE Ch. 2.2 - Prob. 24WE Ch. 2.2 - Prob. 25WE Ch. 2.2 - Prob. 26WE Ch. 2.2 - Prob. 27WE Ch. 2.2 - Prob. 28WE Ch. 2.2 - Prob. 29WE Ch. 2.2 - Prob. 30WE Ch. 2.2 - Prob. 31WE Ch. 2.2 - Prob. 32WE Ch. 2.2 - Prob. 33WE Ch. 2.2 - Prob. 34WE Ch. 2.2 - Prob. 35WE Ch. 2.2 - Prob. 36WE Ch. 2.3 - Prob. 1OE Ch. 2.3 - Prob. 2OE Ch. 2.3 - Prob. 3OE Ch. 2.3 - Prob. 4OE Ch. 2.3 - Prob. 5OE Ch. 2.3 - Prob. 6OE Ch. 2.3 - Prob. 7OE Ch. 2.3 - Prob. 8OE Ch. 2.3 - Prob. 9OE Ch. 2.3 - Prob. 10OE Ch. 2.3 - Prob. 11OE Ch. 2.3 - Prob. 12OE Ch. 2.3 - Prob. 13OE Ch. 2.3 - Prob. 14OE Ch. 2.3 - Prob. 15OE Ch. 2.3 - Prob. 16OE Ch. 2.3 - Prob. 1MRE Ch. 2.3 - Prob. 2MRE Ch. 2.3 - Prob. 3MRE Ch. 2.3 - Prob. 4MRE Ch. 2.3 - Prob. 5MRE Ch. 2.3 - Prob. 6MRE Ch. 2.3 - Prob. 7MRE Ch. 2.3 - Prob. 8MRE Ch. 2.3 - Prob. 9MRE Ch. 2.3 - Prob. 10MRE Ch. 2.3 - Prob. 1ST Ch. 2.3 - Prob. 2ST Ch. 2.3 - Prob. 3ST Ch. 2.3 - Prob. 4ST Ch. 2.3 - Prob. 5ST Ch. 2.3 - Prob. 6ST Ch. 2.3 - Prob. 7ST Ch. 2.4 - Prob. 1OE Ch. 2.4 - Prob. 2OE Ch. 2.4 - Prob. 3OE Ch. 2.4 - Prob. 4OE Ch. 2.4 - Prob. 5OE Ch. 2.4 - Prob. 6OE Ch. 2.4 - Prob. 7OE Ch. 2.4 - Prob. 8OE Ch. 2.4 - Prob. 9OE Ch. 2.4 - Prob. 10OE Ch. 2.4 - Prob. 11OE Ch. 2.4 - Prob. 1WE Ch. 2.4 - Prob. 2WE Ch. 2.4 - Prob. 3WE Ch. 2.4 - Prob. 4WE Ch. 2.4 - Prob. 5WE Ch. 2.4 - Prob. 6WE Ch. 2.4 - Prob. 7WE Ch. 2.4 - Prob. 8WE Ch. 2.4 - Prob. 9WE Ch. 2.4 - Prob. 10WE Ch. 2.4 - Prob. 11WE Ch. 2.4 - Prob. 12WE Ch. 2.4 - Prob. 13WE Ch. 2.4 - Prob. 14WE Ch. 2.4 - Prob. 15WE Ch. 2.4 - Prob. 16WE Ch. 2.4 - Prob. 17WE Ch. 2.4 - Prob. 18WE Ch. 2.4 - Prob. 19WE Ch. 2.4 - Prob. 20WE Ch. 2.4 - Prob. 21WE Ch. 2.4 - Prob. 22WE Ch. 2.4 - Prob. 23WE Ch. 2.4 - Prob. 24WE Ch. 2.4 - Prob. 25WE Ch. 2.4 - Prob. 26WE Ch. 2.4 - Prob. 27WE Ch. 2.4 - Prob. 28WE Ch. 2.4 - Prob. 29WE Ch. 2.4 - Prob. 30WE Ch. 2.4 - Prob. 31WE Ch. 2.4 - Prob. 32WE Ch. 2.4 - Prob. 33WE Ch. 2.4 - Prob. 34WE Ch. 2.4 - Prob. 1CE Ch. 2.4 - Prob. 2CE Ch. 2.5 - Prob. 1OE Ch. 2.5 - Prob. 2OE Ch. 2.5 - Prob. 3OE Ch. 2.5 - Prob. 4OE Ch. 2.5 - Prob. 5OE Ch. 2.5 - Prob. 6OE Ch. 2.5 - Prob. 7OE Ch. 2.5 - Prob. 8OE Ch. 2.5 - Prob. 9OE Ch. 2.5 - Prob. 10OE Ch. 2.5 - Prob. 11OE Ch. 2.5 - Prob. 12OE Ch. 2.5 - Prob. 13OE Ch. 2.5 - Prob. 14OE Ch. 2.5 - Prob. 15OE Ch. 2.5 - Prob. 16OE Ch. 2.5 - Prob. 17OE Ch. 2.5 - Prob. 18OE Ch. 2.5 - Prob. 19OE Ch. 2.5 - Prob. 20OE Ch. 2.5 - Prob. 21OE Ch. 2.5 - Prob. 22OE Ch. 2.5 - Prob. 23OE Ch. 2.5 - Prob. 24OE Ch. 2.5 - Prob. 1WE Ch. 2.5 - Prob. 2WE Ch. 2.5 - Prob. 3WE Ch. 2.5 - Prob. 4WE Ch. 2.5 - Prob. 5WE Ch. 2.5 - Prob. 6WE Ch. 2.5 - Prob. 7WE Ch. 2.5 - Prob. 8WE Ch. 2.5 - Prob. 9WE Ch. 2.5 - Prob. 10WE Ch. 2.5 - Prob. 11WE Ch. 2.5 - Prob. 12WE Ch. 2.5 - Prob. 13WE Ch. 2.5 - Prob. 14WE Ch. 2.5 - Prob. 15WE Ch. 2.5 - Prob. 16WE Ch. 2.5 - Prob. 17WE Ch. 2.5 - Prob. 18WE Ch. 2.5 - Prob. 19WE Ch. 2.5 - Prob. 20WE Ch. 2.5 - Prob. 21WE Ch. 2.5 - Prob. 22WE Ch. 2.5 - Prob. 23WE Ch. 2.5 - Prob. 24WE Ch. 2.5 - Prob. 25WE Ch. 2.5 - Prob. 26WE Ch. 2.5 - Prob. 27WE Ch. 2.5 - Prob. 28WE Ch. 2.5 - Prob. 29WE Ch. 2.5 - Prob. 30WE Ch. 2.5 - Prob. 31WE Ch. 2.5 - Prob. 32WE Ch. 2.5 - Prob. 33WE Ch. 2.5 - Prob. 1MRE Ch. 2.5 - Prob. 2MRE Ch. 2.5 - Prob. 3MRE Ch. 2.5 - Prob. 4MRE Ch. 2.5 - Prob. 5MRE Ch. 2.5 - Prob. 6MRE Ch. 2.5 - Prob. 7MRE Ch. 2.5 - Prob. 8MRE Ch. 2.5 - Prob. 9MRE Ch. 2.5 - Prob. 1ST Ch. 2.5 - Prob. 2ST Ch. 2.5 - Prob. 3ST Ch. 2.5 - Prob. 4ST Ch. 2.5 - Prob. 5ST Ch. 2.5 - Prob. 6ST Ch. 2.5 - Prob. 1E Ch. 2.5 - Prob. 2E Ch. 2.5 - Prob. 3E Ch. 2.5 - Prob. 4E Ch. 2.5 - Prob. 5E Ch. 2.5 - Prob. 6E Ch. 2.5 - Prob. 7E Ch. 2.5 - Prob. 8E Ch. 2.6 - Prob. 1OE Ch. 2.6 - Prob. 2OE Ch. 2.6 - Prob. 3OE Ch. 2.6 - Prob. 4OE Ch. 2.6 - Prob. 5OE Ch. 2.6 - Prob. 6OE Ch. 2.6 - Prob. 7OE Ch. 2.6 - Prob. 8OE Ch. 2.6 - Prob. 1WE Ch. 2.6 - Prob. 2WE Ch. 2.6 - Prob. 3WE Ch. 2.6 - Prob. 4WE Ch. 2.6 - Prob. 5WE Ch. 2.6 - Prob. 6WE Ch. 2.6 - Prob. 7WE Ch. 2.6 - Prob. 8WE Ch. 2.6 - Prob. 9WE Ch. 2.6 - Prob. 10WE Ch. 2.6 - Prob. 11WE Ch. 2.6 - Prob. 12WE Ch. 2.6 - Prob. 13WE Ch. 2.6 - Prob. 14WE Ch. 2.6 - Prob. 15WE Ch. 2.6 - Prob. 16WE Ch. 2.6 - Prob. 17WE Ch. 2.6 - Prob. 18WE Ch. 2.6 - Prob. 19WE Ch. 2.6 - Prob. 20WE Ch. 2.6 - Prob. 21WE Ch. 2.6 - Prob. 22WE Ch. 2.6 - Prob. 23WE Ch. 2.6 - Prob. 24WE Ch. 2.6 - Prob. 25WE Ch. 2.7 - Prob. 1OE Ch. 2.7 - Prob. 2OE Ch. 2.7 - Prob. 3OE Ch. 2.7 - Prob. 1WE Ch. 2.7 - Prob. 2WE Ch. 2.7 - Prob. 3WE Ch. 2.7 - Prob. 4WE Ch. 2.7 - Prob. 5WE Ch. 2.7 - Prob. 6WE Ch. 2.7 - Prob. 7WE Ch. 2.7 - Prob. 8WE Ch. 2.7 - Prob. 9WE Ch. 2.7 - Prob. 10WE Ch. 2.7 - Prob. 11WE Ch. 2.7 - Prob. 12WE Ch. 2.7 - Prob. 13WE Ch. 2.7 - Prob. 14WE Ch. 2.7 - Prob. 15WE Ch. 2.7 - Prob. 16WE Ch. 2.7 - Prob. 17WE Ch. 2.7 - Prob. 18WE Ch. 2.7 - Prob. 1MRE Ch. 2.7 - Prob. 2MRE Ch. 2.7 - Prob. 3MRE Ch. 2.7 - Prob. 4MRE Ch. 2.7 - Prob. 5MRE Ch. 2.7 - Prob. 6MRE Ch. 2.7 - Prob. 7MRE Ch. 2.7 - Prob. 8MRE Ch. 2.7 - Prob. 9MRE Ch. 2.7 - Prob. 1ST Ch. 2.7 - Prob. 2ST Ch. 2.7 - Prob. 3ST Ch. 2 - Prob. 1CR Ch. 2 - Prob. 2CR Ch. 2 - Prob. 3CR Ch. 2 - Prob. 4CR Ch. 2 - Prob. 5CR Ch. 2 - Prob. 6CR Ch. 2 - Prob. 7CR Ch. 2 - Prob. 8CR Ch. 2 - Prob. 9CR Ch. 2 - Prob. 10CR Ch. 2 - Prob. 11CR Ch. 2 - Prob. 12CR Ch. 2 - Prob. 13CR Ch. 2 - Prob. 1CT Ch. 2 - Prob. 2CT Ch. 2 - Prob. 3CT Ch. 2 - Prob. 4CT Ch. 2 - Prob. 5CT Ch. 2 - Prob. 6CT Ch. 2 - Prob. 7CT Ch. 2 - Prob. 8CT Ch. 2 - Prob. 9CT Ch. 2 - Prob. 10CT Ch. 2 - Prob. 11CT Ch. 2 - Prob. 12CT Ch. 2 - Prob. 13CT Ch. 2 - Prob. 14CT Ch. 2 - Prob. 15CT Ch. 2 - Prob. 16CT Ch. 2 - Prob. 1E Ch. 2 - Prob. 2E Ch. 2 - Prob. 3E Ch. 2 - Prob. 4E Ch. 2 - Prob. 5E Ch. 2 - Prob. 6E Ch. 2 - Prob. 7E Ch. 2 - Prob. 8E Ch. 2 - Prob. 9E Ch. 2 - Prob. 10E Ch. 2 - Prob. 11E Ch. 2 - Prob. 12E Ch. 2 - Prob. 13E Ch. 2 - Prob. 14E Ch. 2 - Prob. 15E Ch. 2 - Prob. 16E Ch. 2 - Prob. 17E Ch. 2 - Prob. 18E Ch. 2 - Prob. 1MPS Ch. 2 - Prob. 2MPS Ch. 2 - Prob. 3MPS Ch. 2 - Prob. 4MPS Ch. 2 - Prob. 5MPS Ch. 2 - Prob. 6MPS Ch. 2 - Prob. 7MPS Ch. 2 - Prob. 8MPS Ch. 2 - Prob. 9MPS Ch. 2 - Prob. 10MPS Ch. 2 - Prob. 11MPS Ch. 2 - Prob. 12MPS Ch. 2 - Prob. 13MPS Ch. 2 - Prob. 14MPS

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The reason for the given proof: ‘If a + a = a , then a = 0 .’

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To explain: The reason for the given proof: ‘If a+a=a , then a=0 .’

Answer to Problem 7OE

Explanation of Solution

Chapter 2 Solutions

Additional Math Textbook Solutions

To explain:

The reason for the given proof:

‘If a+a=a , then a=0 .’