Chapter 2: Q58. (page 108)

REASONING Determine whether the following statements are sometimes, always, or never true, if c is an integer. Explain your reasoning.
The solution of $|x + c| = 0$ is greater than 0.

Short Answer

Expert verified

The given statement is ‘never’ true.

Step by step solution

Step-1. Write down the given statement.

The given statement is:

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

Therefore, the given statement is ‘NEVER’ true.

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REASONING Determine whether the following statements are sometimes, always, or never true, if c is an integer. Explain your reasoning.
The solution of $|x + c| = 0$ is greater than 0.

Short Answer

Step by step solution

Step-1. Write down the given statement.

Step-2. Evaluate the given.

Step-3. Conclusion from the statement.

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REASONING Determine whether the following statements are sometimes, always, or never true, if c is an integer. Explain your reasoning.The solution ofx+c=0 is greater than 0.

Short Answer

Step by step solution

Step-1. Write down the given statement.

Step-2. Evaluate the given.

Step-3. Conclusion from the statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Pure Maths

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

REASONING Determine whether the following statements are sometimes, always, or never true, if c is an integer. Explain your reasoning.
The solution of $|x + c| = 0$ is greater than 0.