Chapter 1.7, Problem 2E

(a)

To determine

To Check: The given statement is true or false.

Answer to Problem 2E

True

Explanation of Solution

Given:

Algebraic expression,

  $x\left(x+1\right)>0$

Calculation:

Let $x+1$ is positive and $x$ is negative,

Then

  $x\left(x+1\right)$ 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 $\left(x+1\right)$ both are negative,

Then

  $x\left(x+1\right)$ 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 $\left(x+1\right)$ both are positive,

Then

  $x\left(x+1\right)$ 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

To Check: The given statement is true or false.

Answer to Problem 2E

True

Explanation of Solution

Given:

Algebraic expression,

  $x\left(x+1\right)>5$

Calculation:

Let $x$ and $\left(x+1\right)$ both greater than 5,

Then

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

Conclusion:

Hence, the given statement is true.