Holt Mcdougal Larson Algebra 2: Student Edition 2012

1st Edition

ISBN: 9780547647159

Author: HOLT MCDOUGAL

Publisher: HOLT MCDOUGAL

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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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Expert Solution & Answer

Chapter 3.6, Problem 40E

Solution

To calculate: The value of x for the equation x−2=32x−2 and also check the extraneous solution.

The resultant answer is x=4 and the extraneous solution is 32 .

Given information:

The equation is x−2=32x−2 .

Formula used:

Raise each side of the equation to the same power.

Calculation:

Write the original equation:

x−2=32x−2

Square each side of the equation,

x−22=32x−22x2−4x+4=32x−2x2−4x+6=32x

Multiply both sides by 2,

2x2−4x+6=32x⋅22x2−8x+12=3x2x2−11x+12=0

Divide the equation into factors,

2x2−8x−3x+12=02xx−4−3x−4=0x−42x−3=0x=4 or 32

Now check x=4 or 32 in the original equation.

x−2=32x−2

Now substitute 4 for x and simplify,

4−2=?32⋅4−22=?6−22=2

Now substitute 32 for x and simplify,

32−2=?32⋅32−2−12=?94−2−12=?14−12≠12

Therefore, the only solution is 4 and the apparent solution 32 is extraneous.

Chapter 3.6, Problem 39E

Chapter 3.6, Problem 41E

Chapter 3 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 3.1 - Prob. 1GP Ch. 3.1 - Prob. 2GP Ch. 3.1 - Prob. 3GP Ch. 3.1 - Prob. 4GP Ch. 3.1 - Prob. 5GP Ch. 3.1 - Prob. 6GP Ch. 3.1 - Prob. 7GP Ch. 3.1 - Prob. 8GP Ch. 3.1 - Prob. 9GP Ch. 3.1 - Prob. 10GP

Ch. 3.1 - Prob. 11GP Ch. 3.1 - Prob. 12GP Ch. 3.1 - Prob. 13GP Ch. 3.1 - Prob. 14GP Ch. 3.1 - Prob. 15GP Ch. 3.1 - Prob. 16GP Ch. 3.1 - Prob. 17GP Ch. 3.1 - Prob. 18GP Ch. 3.1 - Prob. 19GP Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - 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Chapter 3 Solutions