# To Check: The given statement 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 1.7, Problem 2E

(a)

To determine

## To Check: The given statement is true or false.

Expert Solution

True

### Explanation of Solution

Given:

Algebraic expression,

x(x+1)>0

Calculation:

Let x+1 is positive and x is negative,

Then

x(x+1) does not greater than zero because multiplication of a positive and negative number will result a negative numberand a negative number always less than zero.

Now, let x and (x+1) both are negative,

Then

x(x+1) is greater than zero because multiplication of two negative number will result a positive number and a positive number always greater than zero.

Now, let x and (x+1) both are positive,

Then

x(x+1) is greater than zero because multiplication of two positive number will result a positive number and a positive number always greater than zero.

Conclusion:

Hence, the given statement is true.

(b)

To determine

Expert Solution

True

### Explanation of Solution

Given:

Algebraic expression,

x(x+1)>5

Calculation:

Let x and (x+1) both greater than 5,

Then

x(x+1) is greater than 5 because multiplication two number always give a increased number.

Conclusion:

Hence, the given statement is true.

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