Q57. - 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 $\left|x+1\right|$ 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 $\left|x+1\right|$ is always greater than zero.

x is an integer.

Step-2. Evaluate the given expression at -1.

Put the value of x as -1 in the given expression:

$\begin{array}{l}=\left|x+1\right|\\ =\left|-1+1\right|\\ =\left|0\right|\\ =0\\ \text{which is not greater than zero.}\end{array}$

Step-3. Conclusion from the statement.

For all the other values of ‘x’, the statement is true, but it is false for $x=-1$.

Therefore, the given statement is ‘SOMETIMES’ true.