Algebra: Structure And Method, Book 1

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 1.3, Problem 40WE

(a)

To determine

To calculate:Number of solutions for the equation using the domain.

(a)

Expert Solution

Answer to Problem 40WE

The number of solutions is “None”.

Explanation of Solution

Given information:

Equation:

x−x=1

Domain for equation:

{1, 2, 3, 4,...}

For x=1 :

1−1=1

That becomes

0=1 (False)

For x=2 :

2−2=1

That becomes

0=1 (False)

For x=3 :

3−3=1

That becomes

0=1 (False)

Since the left side is always zero, there are no solutions.

Thus,

The number of solutions is “None”.

(b)

To determine

To calculate:Number of solutions for the equation with use of the domain.

(b)

Expert Solution

Answer to Problem 40WE

There is “More than one” solution.

Explanation of Solution

Given information:

Equation:

x+x=2x

Domain for equation:

{1, 2, 3, 4,...}

For x=1 :

1+1=2(1)

That becomes

2=2 (True)

For x=2 :

2+2=2(2)

That becomes

4=4 (True)

Since both x=1 and x=2 work,

There is “More than one” solution.

(c)

To determine

To calculate:Number of solutions for the equation with the help of the domain.

(c)

Expert Solution

Answer to Problem 40WE

The number of solutions is “None”.

Explanation of Solution

Given information:

Equation:

x−x=2x

Domain for equation:

{1, 2, 3, 4,...}

For x=1 :

1−1=2(1)

That becomes

0=2 (False)

For x=2 :

2−2=2(2)

That becomes

0=4 (False)

For x=3 :

3−3=2(3)

That becomes

0=6 (False)

Since the left side is always zero, there are no solutions.

Thus,

The number of solutions is “None”.

Chapter 1.3, Problem 39WE

Chapter 1.3, Problem 41WE

Chapter 1 Solutions

Algebra: Structure And Method, Book 1

Ch. 1.1 - Prob. 1OE Ch. 1.1 - Prob. 2OE Ch. 1.1 - Prob. 3OE Ch. 1.1 - Prob. 4OE Ch. 1.1 - Prob. 5OE Ch. 1.1 - Prob. 6OE Ch. 1.1 - Prob. 7OE Ch. 1.1 - Prob. 8OE Ch. 1.1 - Prob. 9OE Ch. 1.1 - Prob. 10OE

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Prob. 38WE Ch. 1.4 - Prob. 39WE Ch. 1.4 - Prob. 40WE Ch. 1.4 - Prob. 41WE Ch. 1.4 - Prob. 42WE Ch. 1.4 - Prob. 43WE Ch. 1.4 - Prob. 44WE Ch. 1.4 - Prob. 45WE Ch. 1.4 - Prob. 46WE Ch. 1.4 - Prob. 47WE Ch. 1.4 - Prob. 48WE Ch. 1.4 - Prob. 49WE Ch. 1.4 - Prob. 50WE Ch. 1.4 - Prob. 51WE Ch. 1.4 - Prob. 52WE Ch. 1.4 - Prob. 53WE Ch. 1.4 - Prob. 54WE Ch. 1.4 - Prob. 1MRE Ch. 1.4 - Prob. 2MRE Ch. 1.4 - Prob. 3MRE Ch. 1.4 - Prob. 4MRE Ch. 1.4 - Prob. 5MRE Ch. 1.4 - Prob. 6MRE Ch. 1.4 - Prob. 7MRE Ch. 1.4 - Prob. 8MRE Ch. 1.4 - Prob. 9MRE Ch. 1.4 - Prob. 10MRE Ch. 1.4 - Prob. 11MRE Ch. 1.4 - Prob. 12MRE Ch. 1.4 - Prob. 13MRE Ch. 1.4 - Prob. 14MRE Ch. 1.5 - Prob. 1OE Ch. 1.5 - Prob. 2OE Ch. 1.5 - Prob. 3OE Ch. 1.5 - Prob. 4OE Ch. 1.5 - Prob. 5OE Ch. 1.5 - Prob. 6OE Ch. 1.5 - Prob. 7OE Ch. 1.5 - Prob. 8OE Ch. 1.5 - Prob. 9OE Ch. 1.5 - Prob. 10OE Ch. 1.5 - Prob. 11OE Ch. 1.5 - Prob. 12OE Ch. 1.5 - Prob. 13OE Ch. 1.5 - Prob. 1WE Ch. 1.5 - Prob. 2WE Ch. 1.5 - Prob. 3WE Ch. 1.5 - Prob. 4WE Ch. 1.5 - Prob. 5WE Ch. 1.5 - Prob. 6WE Ch. 1.5 - Prob. 7WE Ch. 1.5 - Prob. 8WE Ch. 1.5 - Prob. 9WE Ch. 1.5 - Prob. 10WE Ch. 1.5 - Prob. 11WE Ch. 1.5 - Prob. 12WE Ch. 1.5 - Prob. 13WE Ch. 1.5 - Prob. 14WE Ch. 1.5 - Prob. 15WE Ch. 1.5 - Prob. 16WE Ch. 1.5 - Prob. 17WE Ch. 1.5 - Prob. 18WE Ch. 1.5 - Prob. 19WE Ch. 1.5 - Prob. 20WE Ch. 1.5 - Prob. 21WE Ch. 1.5 - Prob. 22WE Ch. 1.5 - Prob. 23WE Ch. 1.5 - Prob. 24WE Ch. 1.5 - Prob. 25WE Ch. 1.5 - Prob. 26WE Ch. 1.5 - Prob. 27WE Ch. 1.5 - Prob. 28WE Ch. 1.5 - Prob. 29WE Ch. 1.5 - Prob. 30WE Ch. 1.5 - Prob. 31WE Ch. 1.5 - Prob. 32WE Ch. 1.5 - Prob. 33WE Ch. 1.5 - Prob. 34WE Ch. 1.5 - Prob. 35WE Ch. 1.5 - Prob. 36WE Ch. 1.5 - Prob. 1MRE Ch. 1.5 - Prob. 2MRE Ch. 1.5 - Prob. 3MRE Ch. 1.5 - Prob. 4MRE Ch. 1.5 - Prob. 5MRE Ch. 1.5 - Prob. 6MRE Ch. 1.5 - Prob. 7MRE Ch. 1.5 - Prob. 8MRE Ch. 1.5 - Prob. 9MRE Ch. 1.5 - Prob. 10MRE Ch. 1.5 - Prob. 11MRE Ch. 1.5 - Prob. 12MRE Ch. 1.6 - Prob. 1P Ch. 1.6 - Prob. 2P Ch. 1.6 - Prob. 3P Ch. 1.6 - Prob. 4P Ch. 1.6 - Prob. 5P Ch. 1.6 - 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Prob. 28MS

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