Q58. - Algebra 1

Question

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

The solution of $\left|x+c\right|=0$ is greater than 0.

Step-by-Step Solution

Answer

The given statement is ‘never’ true.

Step-1. Write down the given statement.

The given statement is:

The solution of $\left|x+c\right|=0$ is greater than 0.

c is an integer.

Step-2. Evaluate the given.

The given expression can be solved as:

Case 1:

$\begin{array}{l}x+c=+0\\ x=0-c\\ x=-c\end{array}$

Case 2:

$\begin{array}{l}x+c=-0\\ x=-0-c\\ x=-c\end{array}$

Step-3. Conclusion from the statement.

The solution of $\left|x+c\right|=0$ is always negative, i.e. -c, hence, it is less than 0 not equal to 0.

Therefore, the given statement is ‘NEVER’ true.