Q60. - Algebra 1

Question

REASONING Determine whether the following statements are sometimes, always, or never true, if c is an integer. Explain your reasoning.

The value of $\left|x+c\right|+c$ is greater than zero.

Step-by-Step Solution

Answer

The given statement is “sometimes” true.

Step-1. Write down the given statement.

The given statement is:

The value of $\left|x+c\right|+c$ is greater than zero.

Step-2. Evaluate the given.

The given statement is sometimes true.

For example:

$\begin{array}{c}\text{Let x = 1 and c = -5;}\\ \left|x+c\right|+c=\left|1-5\right|-5\\ =\left|-4\right|-5\\ =4-5\\ =-1\end{array}$

Here, the answer is not greater than zero.

$\begin{array}{c}\text{Let x = 1 and c = 2;}\\ \left|x+c\right|+c=\left|1+2\right|+2\\ =\left|3\right|+2\\ =3+2\\ =5\end{array}$

Here, the answer is greater than zero.

Step-3. Conclusion from the statement.

The statement is sometimes true.