Chapter 5, Problem 24MCQ

To determine

To find: If the given statement is sometimes, always or never true if $c$ is an integer.

Answer to Problem 24MCQ

The given statement is sometimes true.

Explanation of Solution

Given information: Statement is that the value of $\left|x+c\right|+c$ is greater than $0$ .

Calculation:

  $\left|x+c\right|+c=0$ , when $x=c=0$ .

  $\left|x+c\right|+c$ can also be less than $0$ .

Example:

Let $x=1andc=-1$

Substituting in expression,

  $\left|1+-1\right|+(-1)=-1$ , which is less than $0$ .

  $\left|x+c\right|+c$ can also be greater than $0$ ,

Example:

Let $x=1andc=1$ .

Substituting in expression,

  $\left|1+1\right|+1=3$ , which is greater than $0$ .

Thus, the given statement is sometimes true.