PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.1, Problem 46E
Solution

a.

The algebraic property illustrated by the equation x+21x+2=1 .

Multiplicative inverse property

Given:

The equation is, x+21x+2=1

Concept Used:

  • The multiplicative inverse of a number n is given by the quotient of 1 and the number n . The product of a number and its multiplicative inverse is 1, that is, n⋅1n=1 .

Calculation:

Note that the given expression x+21x+2=1 is of the form of n⋅1n=1 .

Hence, it illustrates the multiplicative inverse property.

b.

The algebraic property illustrated by the equation 1⋅x+y=x+y .

Multiplicative identity property

Given:

The equation is, 1⋅x+y=x+y

Concept Used:

  • Multiplicative identity property a⋅1=1⋅a=a .

Calculation:

Note that the given expression 1⋅x+y=x+y is of the form of a⋅1=1⋅a=a .

Hence, it illustrates the multiplicative identity property.

c.

The algebraic property illustrated by the equation 2x−y=2x−2y .

Distributive property of multiplication over subtraction

Given:

The equation is, 2x−y=2x−2y

Concept Used:

  • Distributive property, a⋅b−c=a⋅b−a⋅c .

Calculation:

Note that the given expression 2x−y=2x−2y is of the form of a⋅b−c=a⋅b−a⋅c .

Hence, it illustrates the distributive property of multiplication over subtraction.

d.

The algebraic property illustrated by the equation 2x+y−z=2x+y−z .

Associative property of addition

Given:

The equation is, 2x+y−z=2x+y−z

Concept Used:

  • Associative property, a+b−c=a+b−c

Calculation:

Note that the given expression 2x+y−z=2x+y−z is of the form a+b−c=a+b−c .

Hence, it illustrates the associative property of addition.

e.

The algebraic property illustrated by the equation 1aab=1aab=1⋅b=b .

Associative property of multiplication, multiplicative inverse, multiplicative identity

Given:

The equation is, 1aab=1aab=1⋅b=b

Concept Used:

  • Associative property, a⋅b⋅c=a⋅b⋅c .

Calculation:

Note that the given expression 1aab=1aab=1⋅b=b illustrates the associative property of multiplication, multiplicative inverse, and multiplicative identity.

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Chapter P.1, Problem 45E
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Chapter P.1, Problem 47E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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