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 41WE

To determine

To calculate: Suppose the domain for each equation is {1,2,3,4,...} . Determine the number of solutions for each equation. Write "None," "One," or "More than one." For those equations with one solution, try to determine what the solution is 4.x=x.4 .

Expert Solution

Answer to Problem 41WE

The given equation has More than one solutions

Explanation of Solution

Given information: The given equation is 4.x=x.4 .

Calculation: Now we try to put the different values from the given set

Let x=1 , then 1.4=4.1=4 , which is true.

Let x=2 , then 2.4=4.2=8 , which is also true

Since more than one value are true so there are more than one solution.

ii.

To determine

To calculate: Suppose the domain for each equation is {1,2,3,4,...} . Determine the number of solutions for each equation. Write "None," "One," or "More than one." For those equations with one solution, try to determine what the solution is 4x=4x+1 .

ii.

Expert Solution

Answer to Problem 41WE

The given equation does not possess any solution, so no solution for the given equation.

Explanation of Solution

Given information: The given equation is 4x=4x+1 .

Calculation: Now we try to put the different values from the given set

Let x=1 , then 4(1)=4(1)+1 , which is false.

Let x=2 , then 4(2)=4(2)+1 , which is also false.

In the given equation right hand side is always 1 greater than left hand side, sothe given equation does not satisfy any value from the given set of values so there no solution.

iii.

To determine

To calculate: Suppose the domain for each equation is {1,2,3,4,...} . Determine the number of solutions for each equation. Write "None," "One," or "More than one." For those equations with one solution, try to determine what the solution is 4.x=8

iii.

Expert Solution

Answer to Problem 41WE

The given equation satisfy only for one value of x , i.e. x=2 from the given set of values so there is One solution for the given equation.

Explanation of Solution

Given information: The given equation is 4x=8 .

Calculation: Now we try to put the different values from the given set

Let x=1 , then 4*1=8 , which is false.

Let x=2 , then 4*2=8 ,which is true.

Let x=3 , then 4*3=8 , which is also false.

Let x=4 , then 4*4=8 , which is also false.

Since the given equation satisfy only for one value of x , i.e. x=2 from the given set of values so there is One solution for the given equation.

Chapter 1.3, Problem 40WE

Chapter 1.3, Problem 42WE

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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Algebra and Trigonometry (6th Edition)

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What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY

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Suppose the domain for each equation is { 1 , 2 , 3 , 4 , ... } . Determine the number of solutions for each equation. Write "None," "One," or "More than one." For those equations with one solution, try to determine what the solution is 4. x = x .4 .

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To calculate: Suppose the domain for each equation is {1,2,3,4,...} . Determine the number of solutions for each equation. Write "None," "One," or "More than one." For those equations with one solution, try to determine what the solution is 4.x=x.4 .

Answer to Problem 41WE

Explanation of Solution

To calculate: Suppose the domain for each equation is {1,2,3,4,...} . Determine the number of solutions for each equation. Write "None," "One," or "More than one." For those equations with one solution, try to determine what the solution is 4x=4x+1 .

Answer to Problem 41WE

Explanation of Solution

To calculate: Suppose the domain for each equation is {1,2,3,4,...} . Determine the number of solutions for each equation. Write "None," "One," or "More than one." For those equations with one solution, try to determine what the solution is 4.x=8

Answer to Problem 41WE

Explanation of Solution

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