PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
10th Edition
ISBN: 9780136174318
Author: 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 62E
Solution

(a)

The two equations 3x+2=5x−7, −2x+2=−7 are equivalent or not.

Yes, the two equations are equivalent.

Given:

The equations, 3x+2=5x−7, −2x+2=−7 .

Concept used:

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

Calculation:

In order to determine the two equations are equivalent or not, first solving first equation and then solving the second one, if they have same solution then these equations are equivalent as shown below:

  first equation3x+2=5x−73x−5x=−7−2−2x=−9x=−9−2x=92Now, 2nd equation −2x+2=−7 −2x=−7−2x=−9−2x=92

So, both the equations have same solution; therefore the two equations are equivalent.

(b)

The two equations 2x+5=x−7, 2x=x−7 are equivalent or not.

Yes, the two equations are equivalent.

Given:

The equations, 2x+5=x−7, 2x=x−7 .

Concept used:

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

Calculation:

In order to determine the two equations are equivalent or not, first solving first equation and then solving the second one, if they have same solution then these equations are equivalent as shown below:

  first equation2x+5=x−72x−x=−7−5x=−12Now, 2nd equation2x=x−72x−x=−7x=−7

So, both the equations have different solution; therefore the two equations are not equivalent.

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Chapter P.3, Problem 61E
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Chapter P.3, Problem 63E

Chapter P Solutions

PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)

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