Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
10th Edition
ISBN: 9780134673301
Author: Waits, Foley, Kennedy, Bock Demana
Publisher: PEARSON
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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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Chapter P.3, Problem 65E
Solution

Which of the given equation in the options are equivalent to the equation 3x+5=2x+1 .

Option (E) 3x=2x−4

Given:

The equations, 3x+5=2x+1 .

The options are

A. 3x=2x

B. 3x=2x+4

C. 32x+52=x+1

D. 3x+6=2x

E. 3x=2x−4

Concept used:

  • The two equations are said to be equivalent when they have the same solution set.

Calculation:

In order to determine the equation which is equivalent to 3x+5=2x+1 equation, first solving the given equation and then solving all the equation given in the option as shown below:

  3x+5=2x+13x−2x=1−5x=−4

Now, solving the equations given in the options as shown below:

  A. 3x=2xx=0B. 3x=2x+43x−2x=4x=4C.  32x+52=x+132x+x=1−52x=−3D.  3x+6=2xx=−6E.  3x=2x−43x−2x=−4x=−4

So, option (E) 3x=2x−4 is equivalent to the equation 3x+5=2x+1 .

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Chapter P.3, Problem 64E
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Chapter P.3, Problem 66E

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

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