# To state: whether the inequality 10 11 &lt; 12 13 is true or false. ### Precalculus: Mathematics for Calcu...

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

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

Expert Solution

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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