PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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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 68E
Solution

Which of the given equation in the options are equivalent to the equation 23x+12=x4−13 .

A. 2x+1=x−1

B. 8x+6=3x−4

C. 4x+3=32x+−2

Given:

The equations, 23x+12=x4−13 .

The options are

A. 2x+1=x−1

B. 8x+6=3x−4

C. 4x+3=32x+−2

D. 4x+3=3x−4

E. 4x+6=3x−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 23x+12=x4−13 equation, first solving the given equation and then solving all the equation given in the option as shown below:

  23x+12=x4−13subtract x4 from both side2x3+12−x4=x4−x4−1312+5x12=−13subtract 12 from both side12−12+5x12=−13−125x12=−56multiply both side by 125x12×12=−56×125x=−10divide both side by 55x5=−105x=−2

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

  A. 2x+1=x−12x−x=−1−1x=−2B. 8x+6=3x−48x−3x=−4−65x=−10x=−2C.  4x+3=3x2−24x−3x2=−2−38x−3x2=−55x2=−5x=−2D.  4x+3=3x−44x−3x=−4−3x=−7E.  4x+6=3x−44x−3x=−4−6x=−10

So, option (A), (B), (C) equation is equivalent to the equation 23x+12=x4−13 .

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Chapter P.3, Problem 67E
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Chapter P.3, Problem 69E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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