BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.1, Problem 34E

(a)

To determine

To state: whether the inequality 1011<1213 is true or false.

Expert Solution

Answer to Problem 34E

  1011<1213 is true.

Explanation of Solution

Given information:

An inequality as 1011<1213 .

Formula used:

For two fractions ab and cd .

  ab<cd if a<c,b=d

For two fractions ab and cd .

  ab>cd if a>c,b=d

For two fractions ab and cd .

  ab=cd if a=c,b=d

Calculation:

Consider the given inequality.

  1011<1213

Now, multiply numerator and denominator of 1011 by 13 and 1213 by 11.

  1011=10×1313×11=1301431213=12×1113×11=132143

Here, for 130143 and 132143 ,

  130<132

Hence, 130143<132143

Hence, the inequality 1011<1213 is true.

(b)

To determine

To state: whether the inequality 12<1 is true or false.

Expert Solution

Answer to Problem 34E

  12<1 is true.

Explanation of Solution

Given information:

An inequality as 12<1 .

Formula used:

For two numbers a and b

  a<b if a>b

For two fractions ab and cd .

  ab<cd if a<c,b=d

For two fractions ab and cd .

  ab>cd if a>c,b=d

For two fractions ab and cd .

  ab=cd if a=c,b=d

Calculation:

Consider the given inequality.

  12<1

Now, multiply numerator and denominator of 1 by 2.

  1=1×21×2=22

Here, for 12 and 22 ,

  1<2

Hence, 12<22

Multiply both sides by (1) .

  12(1)<22(1)12>2212>1

Hence, the inequality 12<1 is false.

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