BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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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 5.4, Problem 55E

To determine

To show: The change in the solution of the given equations.

Expert Solution

Answer to Problem 55E

For, x−4=2x,x=8 .

For , x−4=−2x,x=2 .

Explanation of Solution

Given information:

The following equations:

x−4=2xx−4=−2x

Calculation:

The equations are solved as follows:

x−4=2x [Given]x−4=(2x)1/2 [Express in exponent form](x−4)2=2x [Raise each side to the second power]x2−8x+16=2x [Expand]x2−10x+16=0 [Subtract 2x from both sides](x−8)(x−2)=0 [Factor]x−8=0 [Set factor to zero]x=8 [Simplify]

x−4=−2x [Given]x−4=(−2x)1/2 [Express in exponent form](x−4)2=2x [Raise each side to the second power]x2−8x+16=2x [Expand]x2−10x+16=0 [Subtract 2x from both sides](x−8)(x−2)=0 [Factor]x−2=0 [Set each factor to zero]x=2 [Simplify]

The factors set to zero in the above evaluations are selected by keeping in mind the sign on other side of the equation.

To determine

To justify: The solutions obtained in part a, using graphs.

Expert Solution

Explanation of Solution

Given information:

The following equations:

x−4=2xx−4=−2x

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press Y= button.

Step 3: Enter the expressions Y1=x−4 , Y2=2x and Y3=−2x which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 5.4, Problem 55E

Interpretation :

From the above graph, it can be observed that for x−4=2x , value of x is 8 and for x−4=−2x , value of x is 2 . Hence the solutions are verified.

Chapter 5.4, Problem 54E

Chapter 5.4, Problem 56E

Chapter 5 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - 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